A SEMI-STRONG FORM EVALUATION OF THE EFFICIENCY OF 
THE WHEAT FUTURES MARKET 
by 
Llewelyn Edward Jones 
A thesis submitted in par~ial fulfillment 
of the requirements for the degree 
of 
Master of Science 
in 
Applied Economics 
MONTANA STATE UNIVERSITY 
Bozeman, Montana 
March 1988 
ii 
APPROVAL 
of a thesis submitted by 
Llewelyn Edward Jones 
This thesis has been read by each member of the thesis committee 
and has been found to be satisfactory regarding content, English usage, 
format, citations, bibliographic style, and consistency, and is ready 
for submission to the College of Graduate Studies. 
Date Chairperson, Graduate Committee 
Approved for the Major Department 
Date Head, Major Department 
Approved for the College of Graduate Studies 
Date Graduate Dean 
j 
iii 
STATEMENT OF PERMISSION TO USE 
In presenting this thesis in partial fulfillment of the 
requirements for a master's degree at Montana State University, 1 agree 
that the Library shall make it available to borrowers under rules of the 
Library. Brief quotations from this thesis are allowable without 
special permission, provided that accurate acknowledgment of source is 
made. 
Permission for extensive quotation from or reproduction of this 
thesis may be granted by my major advisor, or in his absence, by the 
Dean of Libraries when, in the opinion of either, the proposed use of 
the material is for scholarly purposes. Any copying or use of the 
material in this thesis for financial gain shall not be allowed without 
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Signature ____________________________ __ 
Date ________________________________ ___ 
iv 
ACKNOWLEDGMENTS 
I would like to express my appreciation to my committee members, 
Dr. Jeffrey T. LaFrance, Dr. Ronald N. Johnson, and Dr. John M. Marsh 
for their patience and guidance during the course of this thesis. 
Special thanks go to my parents, Edward and Marjorie, and my wife, 
Carole, whose love and support made possible the pursuit and attainment 
of my academic goals. 
v 
TABLE OF CONTENTS 
Page 
APPROVAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i 
STATEMENT OF PERMISSION TO USE............................. iii 
ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i v 
TABLE OF CONTENTS..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 
LIST OF TABLES............................................. vii 
LIST OF FIGURES............................................ viii 
ABSTRACT................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i x 
CHAPTER 
1 . INTRODUCTION .................................... . 
I nt reduction ................................. . 
Statement of the Problem ..................... . 
Objectives ................................... . 
2. REVIEW OF THE LITERATURE ........................ . 
The Theory of Efficient Markets .............. . 
Efficient Futures Market Research ............ . 
Wheat Price Forecasting Models ............... . 
General Autoregressive Integrated Moving 
Average Modeling Theory ...................... . 
Development of an Efficiency Test for the 
Wheat Futures Market ......................... . 
Data Availability and Requirements ........... . 
3. EMPIRICAL RESULTS ............................... . 
Soft Red Winter Wheat ARIMA Model ............ . 
Random Walk Model Results ................. . 
ARIMA(3,0,3) Model Results ................ . 
USDA Model Results ........................... . 
1 
2 
3 
5 
5 
12 
17 
21 
25 
29 
31 
31 
31 
40 
50 
Vi 
TABLE OF CONTENTS-Continued 
Page 
Market Trader's Model Results................. 55 
Predicting the PPI............................ 59 
Utilizing the ARIMA(3,0,3) Model.............. 60 
4. SUMMARY AND CONCLUSIONS .........................• 66 
Summary....................................... 66 
Cone 1 us ions. . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . 69 
Further Research.............................. 70 
BIBLIOGRAPHY............................................... 72 
APPENDIX ....••................•.•....•.....•......... ·..•... 76 
vi i 
LIST OF TABLES 
Table Page 
1. Price Predictions with a Random Walk Model ....... . 37 
2. Predictions Made by the Wheat Futures Market ..... . 38 
3. Autocorrelation Check of Residuals ............... . 44 
4. Price Predictions with an ARIMA(3,0,3) Model ..... . 48 
5. Price Predictions with Model (23) ................ . 53 
6. Price Predictions with the Market Trader's 
Mode 1 ............................................ . 57 
7. PPI Predictions with a Random Walk Model ......... . 60 
8. Returns to Market Price Speculation Using 
the ARIMA(3,0,3) Model ........................... . 63 
9. Original Data Set ................................ . 11 
viii 
LIST OF FIGURES 
Figure Page 
1. Relationship Between Quarterly Prices and 
Stocks-to-Use Ratio ............................. . 19 
2. Nominal and Real Cash Soft Red Winter Wheat ..... . 32 
3. Random Walk Model's Forecast versus Cash 
Price ........................................... . 40 
4. Wheat Futures Market's Forecast versus Cash 
Price ........................................... . 41 
5. Autocorrelation Function (ACF) for Cash Wheat .... 42 
6. Partial Autocorrelation Function (PACF) for 
Cash Wheat ...................................... . 43 
7. ARIMA(3,0,3) Model's Forecast versus Cash 
Price ................................... ·· .. ··.·· 49 
8. USDA Model's Forecast versus cash Price ......... . 54 
9. Market Trader's Model's Forecast versus Cash 
Price ........................................... . 58 
~ 
ix 
ABSTRACT 
Futures market efficiency is of concern to both market participants 
and non-participants. The practical problem is that inefficient futures 
markets can lead to resource allocation problems. The specific objective 
of this study is to perform a Fama (1970) semi-strong efficiency test on 
the Chicago Board of Trade's wheat futures market. 
In this study, three wheat price prediction models are used as a 
standard with which to compare, on the basis of root mean squared error 
and bias, the futures market. One of the models, an autoregressive 
integrated moving average model, succeeded in obtaining a semi-strong 
efficiency rejection. Returns from speculating with the autoregressive 
integrated moving average model are then examined to see if the 
incremental returns are sufficiently large to cover all costs of 
speculating. A 19.5 percent after cost return was generated by 
simulating speculation with this model. Since a risk premium is 
expected when using unproven methods to forecast price, it was not 
determined whether this return is large enough to compensate for the 
risks involved. 
The results of this study indicate that there exists a possibility 
that the Chicago Board of Trade's wheat futures market is not allocating 
resources efficiently, at least for the time frame examined and 
efficiency definition chosen. As to whether this detected ineff~ciency 
is just an anomaly caused by the time frame examined, efficiency 
definition chosen, or the examination method, little can be said. The 
results of this test are only strictly interpreted relative to the 
particular definition of efficiency and time period chosen, and are not 
used to infer that the futures market can be replaced by a "more 
efficient" m~rketing tool. 
1 
CHAPTER 1 
INTRODUCTION 
Introduction 
This study offers a semi-strong test of the efficiency of the 
Chicago Board of Trade's wheat futures market. Specifically, the study 
compares the Chicago Board of Trade's wheat futures markets quarterly 
price predictions with predictions made by autoregressive integrated 
moving average (ARIMA), United Stated Department of Agriculture (USDA), 
and market trader's models. The basts for comparison is root mean 
squared error CRMSE) and bias. The approach follows the format set 
forth by Leuthold and Hartman's (1979) analysis of the Chicago Board of 
Trade's hog futures market with the exception that the structural models 
used to forward price predict in this study were chosen from the 
literature rather than explicitly created from economic analysis. 
Choosing models from the literature allows conclusions about the forward 
price predicting ability of commonly accepted models while avoiding 
questions of model specification validity. 
Following Fama (1970, p. 1), the definition of efficiency 
explicitly tested in this study is, "A market in which prices fully 
reflect available information is called efficient." This definition was 
made testable by Fama (1970) and is the model of choice for studies such 
as these. Upon completion of this study some conclusions about wheat 
2 
futures market efficiency and model choice are reached for the period 
1966 to 1986. 
Statement of the Problem 
Grain production and export trade is of tremendous importance to 
the United States; the United States produces 141 of the world's grain 
and exports SOl of the world's grain trade (Cramer et al., 1983). The 
futures markets play an integral part in this grain trade with the 
number of contracts traded increasing fifteen fold from 1960 to 1985. 
Presently, there are approximately 9000 contracts traded per day <Peck, 
1985). The Chicago Board of Trade's wheat futures market is generally 
considered the key grain futures market for two reasons: (1) the largest 
volume of grain futures trading, approximately 75% of the total grain 
futures trade, occurs on the Chicago Board of Trade; and (2) while the 
contracts tendered on the Chicago Board of Trade are for soft red winter 
wheat, other grain varieties such as soft white wheat, hard red winter 
wheat, and hard red spring wheat are accepted for delivery with the 
appropriate premiums and discounts. 
The above statements demonstrate the prominent role that grain 
futures trading plays in the United States economy. A question of 
concern to participants in this market is whether or not this market is 
operating efficiently since an inefficient market could potentially lead 
to the misallocation of resources. This question is also important to 
individuals that may not directly participate in the wheat futures 
market, but still use the wheat futures market's forward pricing 
function to make decisions. 
3 
The procedure for testing a market for pricing efficiency must take 
into consideration the cost and availability of any models that are 
chosen for comparison. For thi~ reason, readily available USDA and 
futures trader's models were selected and modeling procedures were 
deliberately kept simple. Upon selection of a "best" competing model, 
hypothetical trading with relevant commission charges will be executed 
over a prospective test period. 
Objectives 
The specific objectives of this research project are: 
1. To test the hypothesis that the Chicago Board of Trade's 
wheat futures market is efficient. 
2. To rank, on the basis of RMSE and bias, USDA, ARMA, and 
futures trader's models. 
3. To test any model(s) that succeed(s) in rejecting the 
hypothesis in objective (1) for after commission above 
average returns where above average returns are defined to 
be returns in excess of the return rate of "safe" 
investments such as cash deposits (CDs) at a bank. 
Organization of this thesis is as follows: the second chapter 
reviews previous research done on futures markets and efficiency, 
summarizes wheat models that are present in the literature, briefly 
develops the theory behind autoregressive integrated moving average 
modeling, and develops a testable implication from the chosen 
definition of efficiency. Chapter 3 presents the empirical results of 
4 
the efficiency tests undertaken. Chapter 4 includes the summary, 
suggestions for further research, and other concluding remarks. 
5 
CHAPTER 2 
REVIEW OF LITERATURE 
This chapter consists of six sections. The first traces the 
development of the theory of efficient markets. The second section 
summarizes previous research done on the subject of efficient futures 
markets. The third section reviews recent literature on wheat price 
models; two of these models will be chosen to use in the efficiency 
tests. The fourth section briefly reviews the theory behind auto­
regressive integrated moving average modeling. The fifth section 
develops the efficiency tests that are to be undertaken in this study. 
The sixth section considers data requirements and availability. The 
list of references cited in this review is not complete. However, it 
does contain those works considered by the author to be important to the 
development and motivation of this project. 
The Theory of Efficient Markets 
Working (1958) writes that the sources of market mistakes are 
information and judgment, and classed market inaccuracies as 
"necessary" and "objectionable." An efficient market contains only 
necessary inaccuracies; unexpected price changes are due only to new 
information. Any error beyond that is objectionable inaccuracy, often 
termed as speculative error, and likely results from the bad judgment of 
traders or from noncompetitive market situations. Working (1949) 
6 
implies that, if future price changes are predictable, objectionable 
inaccuracies must exist. If the changes are unpredictable, 
objectionable error is absent. Samuelson (1965, p. 105) followed this 
line of reasoning when he noted that "expected profits in an efficient 
market can't be increased by charts or any other esoteric device of 
magic or mathematics." 
Fama (1970) took general statements such as the ones above, and, in 
an article that has become a classic in the relevant literature, defined 
concise tests for market efficiency. First, Fama (1970) stated the 
following sufficient conditions for market efficiency: (1) there are no 
transaction costs involved in trading; (2) all available information is 
costlessly available to all market participants; and (3) all agree on 
the implications of current information for the current market price and 
distributions of future market prices. In such a market, the current 
market price would obviously "fully reflect" all available information. 
However, while the above conditions are sufficient for market 
efficiency, they are not necessary. The market may still be efficient 
if "sufficient numbers" of investors have access to available 
information, and there are no investors who can consistently make better 
evaluations of available information than are implicit in market prices 
CFama 1970). Next, Fama (1970) concisely defined an efficient market as 
one in which prices "fully reflect" all available information. Then 
Fama (1970) defined exactly what he meant by the term "fully ·reflect". 
His theoretical development went as follows: 
- -(1) E ( p .J • t: + 1 lit ) = [ 1 + E ( r .J • t + 1 : It: ) l p .J t , 
where E is the expected value operator, P.Jt: is the price of security j 
7 
at time t, P.:t,t+l is its price at t+l (With reinvestment of any 
intermediate cash income from the security), G,t+l is the one-period 
percentage return (P.:t.t+l - P.:~tliP.:~t• It is a general symbol for 
whatever set of information is assumed to be "fully reflected" in the 
price at t, and the tildes indicate that Pt • .J+l and r.J,t+l are random 
variables at t. The value of the equilibrium expected return 
ECr.:~.t• 1 1ft> projected on the information It would be determined from 
the particular expected return theory at hand. The conditional 
expectation notation of (1) is meant to imply, however, that whatever 
expected return model is assumed to apply, the information in It is 
fully utilized in determining equilibrium expected returns. This is the 
sense in which It is "fully reflected" in the information of the price 
P.:tt · 
Fama (1970) then took his equation (1) and developed some 
empirically testable implications. His development went as follows: The 
assumptions that the conditions of market equilibrium can be stated in 
terms of expected returns and that equilibrium expected returns are 
formed on the basis of (and thus "fully reflect") the information set It 
have a major empirical implication-- they rule out the possibility of 
trading systems based only on the information in It that have expected 
profits or returns in excess of equilibrium expected profits or returns. 
Thus let 
(2) X .:I • t + 1 = p .:I • t + 1 - E ( p .:I • t + 1 lit ) 
Then 
-( 3) E(X.:t,t+ 1 lit) = 0 
which, by definition, says that the sequence {x.:tt J is a "fair game" with 
8 
respect to the information sequence {It}. or, equivalently, let 
-(4) z.J.t+1 = r.J.t+1 - E(r.J.t+1 :tt J 
Then 
( 5) ECz.J.t+1 :tt> = o, 
so that the sequence £z.Jtl is also a fair game with respect to the 
information sequence £1}. 
In economic terms, x.J. t+l is the excess market value of security 
j at time t+l; it is the difference between the observed price and the 
expected value of the price that was projected at t on the basis of the 
information It· Similarly, z.J.t+l is the return at t+1 in excess of the 
equilibrium expected return projected at t. Let 
(6) a ( It > = C a1 ( It > , ~ ( It: ) , ... , C4. ( It: > J 
be any trading system based on It which tells the investor the amounts 
a.J(It> of funds available at t that are to be invested in each of then 
available securities. The total excess market value at t+l that will be 
generated by such a system is 
( 7) 
n 
vt+l = s a.J Cit: Hr.J.t+l - ECr.J.t+l a~ )Ji, 
..:1-1 
which, from the fair game property of (5) has expectation, 
- n ( 8) E(Vt:+l :tt:) = 5 a..t Cit )E(z.J.t+1 :tt) = 0 . 
..:1-1 
The testable implications of Fama's (1970) work are quite 
straightforward. It is impossible to create a model that outpredicts an 
efficient market to the extent that expected profits or returns in 
excess of "normal" profits or returns are generated. 
9 
Fama (1970) broke the tests of efficient markets into three 
categories. These categories were named weak form test, semi-strong 
form test, and strong form test in order to reflect Fama's judgment 
of how powerful each efficiency test was. 
The first category, the weak form test for efficiency, requires 
testing a market to see if price changes follow a random walk. A random 
walk implies that successive price changes (or successive one-period 
returns) are independent and identically distributed. Formally, this 
says 
(9) f( r .J. t: ... 1 I It: ) = f ( r .J • t: +1 > , 
which is the usual statement that the conditional and marginal 
probability distributions uf an independent random variable are 
identical. In addition, the density function f must be the same for all 
t. Expression (9), of course, says much more than the general expected 
return model summarized by (1). For example, if we restrict (1) by 
assuming that the expected return on securttiy j is constant over time, 
then we have 
-( 10) E(r.J.t:+ 1 11t:l = E(r.J.t:+ 1 ). 
This says that the mean of the distribution of r.J.t:+l is independent of 
·the information available at t, It:, whereas the random walk model of (9) 
says in addition that the entire distribution is independent of It:. 
This, however, does not preclude the possibility of a trend (random 
walk with a drift) since expected price changes can be non-zero; earlier 
work by samuelson (1965) had previously shown that prices could follow 
deterministic trends while still fluctuating randomly. Fama (1970) was 
careful to note that, as shown above, the fair game assumption is not 
10 
sufficient to lead to a random walk. The random walk implies much more, 
i.e. that the expected return (indeed the entire distribution of 
returns) be stationary (zero serial correlations) through time. 
However, while zero serial correlations are consistent with the "fair 
game" model, the "fair game" model does not specifically require zero 
serial correlations. In his 1970 article, Fama did show that many 
markets that tested "fair game" efficient were serially correlated. 
However, he felt that the small levels of serial correlation that seem 
to be often present in markets could not very likely be exploited for 
profitable returns. Fama (1970) went on to explain that it is probably 
best to regard the random walk model as a special case of the more 
general expected return model ("fair game" model) in the sense of making 
a more detailed specification of the economic environment. That is, the 
basic model of market equilibrium is the "fair game" expected return 
model, with a random walk arising when additional environmental 
conditions 
time. From 
assumption 
are such that one-period returns repeat themselves through 
this viewpoint, violations of the pure independence 
of the random walk model are to be expected. But, when 
judged relative to the benchmark provided by the random walk model, 
these violations can provide insights into the nature of the market 
environment. Fama (1970) concluded his section on weak form tests by 
noting that there isn't much evidence against the "fair game" model's 
more ambitious offspring, the random walk. 
Fama's (1970) second category, the semi-strong form tests, 
contains tests of efficient market that are concerned with whether 
current prices "fully reflect" all obvious publicly available 
11 
information. Each individual test is concerned with the adjustment of 
market prices to some kind of information generating event(s) (e.g., 
export reports, domestic usage, dollar values, substitute prices, etc.). 
Leuthold and Hartmann (1979) interpreted this test to include 
comparisons between econometric models and futures markets; if an 
econometric model better utilizes available information and thereby 
out-forecasts the futures market in question, then this is a valid semi-
strong rejection of market efficiency. When semi-strong tests of 
efficiency are carried out in this manner, the econometric models become 
a norm with which to compare the futures markets. 
Fama~s (1970) third category, the strong form test, contains tests 
of efficient markets that are concerned with whether current prices 
"fully reflect" all available information. Fama (1970, p. 415) noted 
that, "The strong efficient markets model, in which prices are assumed 
to reflect all available information, is probably best viewed as a 
benchmark against which deviations from market efficiency (interpreted 
in its strictest sense) can be judged." Tests that fall into this 
category would be concerned with above average returns being generated 
by such factors as monopolistic access to information. 
Osborne (1966) and Scholes (1969) indicated that 
Niederhoffer and 
such market 
inefficiencies do occur by showing that above average returns are earned 
by New York Stock Exchange specialists and corporate officers. 
Since Fama (1970), there have been many articles dealing with the 
concept of efficiency and the characteristics of efficient markets. The 
conventional Fama (1970) approach to efficiency was taken by this 
author, so little discussion will be made of later approaches. It is 
12 
pertinent to note, however, that later works do indicate that there may 
be some problems with Fama's (1970) definition of efficiency since no 
account is taken of the costs of acquiring information and/or changes in 
the variability of the price series (Grossman and Stiglitz, 1980). In 
fact, Grossman and Stiglitz (1980) showed that, for the property of 
efficiency to hold, costless information is not only a sufficient 
condition, but also a necessary condition. This implies that, even if a 
particular model's forecast is more accurate than the forecasts of the 
futures market, inefficiency does not necessarily follow. For a market 
to be inefficient, it is necessary to have a model that forecasts more 
accurately than the market; however, this is not sufficient for market 
inefficiency. To be sufficient for market inefficiency, the risk 
adjusted returns must be large enough to cover all modeling costs. 
Efficient Futures Market Research 
Both the efficient market model and the special random walk model 
discussed in the previous section imply that no mechanical trading rules 
can be used to increase profits. A large body of research that followed 
Fama's (1970) article attempted to reject efficiency by constructing 
successful trading rules or by testing for serial correlations with the 
idea that serial correlations indicate the possibility of profitable 
trading rules. Since this will largely be the approach taken in this 
study, the articles discussed in the following section will be 
congregated around these ideas. Other approaches to efficiency tests of 
futures markets do exist and will be briefly summarized at the end of 
this section. 
13 
cargill and Rausser (1975, p. 1049) weak form efficiency tested 
464 futures contracts from seven commodities (corn, oats, soybeans, 
wheat, copper, live beef cattle, and pork bellies) and obtained weak­
form rejections of efficiency for the set of results as a whole: "the 
results of this analysis clearly indicate that there are a significant 
number of departures from randomness. Thus the random walk model must be 
rejected." They did note in their paper that this was a rejection of a 
random walk and therefore did not necessarily imply that the markets 
tested were inefficient. In fact, in an interesting aside in their 
paper, they applied a g-percent filter (a quite popular trading rule 
that gives buy-sell signals based upon percentage changes in price) to 
computer produced random series of market prices and succeeded in 
generating substantial profits. Cargill and Rausser (1975) felt that 
this was strong evidence in support of the contentions that the random 
walk model was not an accurate explanation of efficient commodity 
markets and that positive profits from the g-percent filter were not 
necessarily indications of serial correlation as previously believed. 
Leuthold and Hartmann (1979) performed a semi-strong form test for 
efficiency on the Chicago Board of Trade's hog futures market by 
constructing an econometric forecasting model to serve as a norm with 
which to compare the Chicago Board of Trade's hog futures market. The 
econometric model was a two equation demand-supply model using monthly 
data and closely following the well known cobweb model. Leuthold and 
Hartmann (1979, p. 484) stated that, "By design, the econometric model 
is kept simple because, if a simple model shows the market to be 
inefficient, further elaboration becomes unnecessary to test the 
I --
14 
efficient market hypothesis." On the basis of RMSE, Leuthold and 
Hartmann (1979) were able to reject (semi-strong form test) the 
efficiency hypothesis. They chose to use RMSE as the statistic of 
comparison because of the importance of weighting large errors greater 
than small errors in a forecasting model. 
Rausser and Carter (1983) performed a semi-strong test of 
efficiency on the Chicago Board of Trade's soybean complex. They 
followed fairly closely the framework set forth by Leuthold and Hartmann 
(1979) by building an econometric forecasting model with which to 
compare the futures market and succeeded in obtaining a semi-strong 
rejection of market efficiency. However, they did not feel that this 
was in fact a true rejection of efficiency; rather, they felt that the 
necessary condition for efficiency rejection had been met. The 
sufficient condition for efficiency rejection would require that the 
cost of constructing 
incremental benefits 
and utilizing their model 
appropriately adjusted 
did 
by 
not exceed the 
risk (relative 
cost/benefit condition). Bias was also added as a comparison statistic 
in Rausser and Carter's (1983) analysis because they felt that for a 
model to meet the necessary condition for efficiency rejection it had to 
do so in both terms of volatility (RMSE) and bias. They referred to 
this concept of meeting both a bias and a volatility constraint as 
"relative accuracy." In concluding their article, Rausser and Carter 
(1983, p. 477) pointed out that, while only the necessary condition for 
efficiency rejection had been quantitatively met by their research, they 
had deliberately kept the predictive models simple, thereby minimizing 
the marginal cost of use and giving a high probability of meeting 
15 
sufficiency requirements for efficiency rejection: "It appears that 
opportunities exist in the soybean complex for excess returns, i.e., 
returns whicn exceed normal returns adjusted for· risk." They did 
indicate that, in later research, they planned to do market trading 
simulations with their model to test if actual excess returns do exist. 
A simple trading rule using their model as an indicator of market 
direction was to be used in developing a trading strategy. 
Kamara (1984) summarized other research that had occurred in the 
futures market efficiency area over the last twenty years. As a whole, 
the results he found were fairly disconcerting since different 
researchers asking the same or similar questions often reached 
different conclusions. In the area of price forecasting ability the 
general consensus was that the speculator, especially the large 
speculator (defined as a speculator who traded in large enough 
quantities that reports on market position and intent had to be filed 
with the Commodity Futures Trading Commission), could forecast pri.ce 
better than the futures market. This result would be consistent with a 
Fama (1970) semi-strong efficiency rejection. However, it should be 
noted that the majority of the studies reviewed by Kamara (1984) did not 
take into account the cost of the speculator's forecasting information 
or the possibility that the speculators were being rewarded for bearing 
risk. Therefore, these results represent only the necessary condition 
for efficiency rejection and do not meet sufficiency requirements. 
Also, it should be noted that Hartzmark, in a 1987 study based upon the 
Commodity Futures Trading Commission's confidential files, was unable to 
16 
find any evidence to support the contention that speculators could 
forecast price. 
As for the special case of the random walk efficiency tests, 
most of the research on random walk models of the futures markets that 
was summarized by Karama (1984) found some evidence of serial 
correlation, especially short run serial correlation. While this result 
is consistent with a Fama (1970) weak form rejection of efficiency, 
again the results aren't very compelling. The mere existence of some 
nonrandom components is not sufficient evidence to reject general 
efficiency unless some unexploited opportunities for above average 
profits are created by this Jack of randomness in price. 
A 1980 argument by Grossman and Stiglitz probably best summarizes 
the current thoughts on futures market efficiency. They argued that if 
futures prices reflected all available information, then traders would 
have no incentive to gather information. If information is costly to 
obtain, then, in equilibrium, prices will reveal only part of the 
information held by informed traders, so that those who acquire 
information earn a higher return. Costly information will result in 
market prices that do not reflect all available information even though 
no traders behave suboptimally. This again emphasizes current 
theoretical trends towards redefining Fama's (1970) efficiency rejection 
tests as tests for only the necessary conditions for efficiency 
rejection and not tests that satisfy general market efficiency rejection 
criterion. 
To meet both necessary and sufficient criterion for efficiency 
rejection, the potential expected returns from exploitation of the 
17 
perceived failings in the market price must be greater than the cost and 
risk of gathering and utilizing the necessary information. 
Wheat Price Forecasting Models 
This section reviews some of the recent models that are used for 
forecasting wheat prices. Only models that were published in commonly 
read or easily available publications were considered as relevant 
1 i terature. This was done to insure that the cost of acquiring and 
using these models was minimal. 
Westcott et al. (1984) and Westcott and Hull (1985) built wheat 
price forecasting models for the United States Department of Agriculture 
(the USDA is the largest publisher of agricultural commodity and price 
forecasts). The model they developed was based on the general 
hyperbolic function, (P-a)(S-d) = c, where P is the quarterly wheat 
price, s denotes quarterly ending stocks of wheat, and a, c, and d are 
parameters. To avoid nonlinearities in estimation, the parameter d was 
assumed to equal zero. Solving the above equation for price gives P = 
a + cs- 1 • To represent the different effects of stocks through the 
year, a separate c parameter was assumed for each quarter. It is 
important to note that stocks, s, were measured relative to amount of 
usage, u, in the wheat industry. Westcott et al. (1984) felt that, 
since the wheat market had grown sharply over time, it was necessary to 
develop this "relative usage" measurement of stocks because a larger 
market required a greater level of stocks to keep marketing channels 
filled. Lagged price was also included as an independent variable to 
reflect short term "stickiness" of quarterly wheat prices. Price 
18 
"stickiness~ was thought to reflect partial adjustments caused by 
relative bargaining positions of market participants and/or expectations 
based upon incomplete market information, which thereby prevented 
complete price adjustments in the short run. The preceding adjustment 
resulted in the following general equation: 
(i 1 ) 4 P =a+ b lag(PJ + s c,D, (5/U)- 1 • 
i=l 
Where o, are quarterly dummy variables (equal to 1 in the i-th quarter, 
0, elsewhere), lag(PJ is the one quarter lag of price (P), and a, b, and 
c,, i=1, ... ,4, are parameters to be estimated. The subscripts "i" 
denote quarters, where 1=1 is the January-March quarter, i=2 is the 
April-May quarter, i=3 is the June-September quarter, and i=4 is the 
October-December quarter. Westcott et al. (1984) included the 
c:~.D:~. (5/U)- 1 terms to allow a different effect of stocks on prices in 
each quarter. Thus, equation (11) is expected to yield a family of four 
hyperbolic curves that represent price's relationship to the stock-to-
use ratio for each quarter (see Figure 1). For any given stock-to-use 
ratio, such as 5°/UO, the resulting prices would be expected to be 
smaller as the time from harvest increases. This is indicated by a 
movement from one hyperbolic curve to the next. The actual model was 
estimated from 1971-81 (44 observations). 
The final empirical results were: 
(12) P = 0.041 + .830 lag(P) + 1.071 01 (5/U)- 1 + .389 02 {5/U)- 1 + (0.2) (12.7) (1.9) (0.9) 
2.385 03 (5/U)- 1 + 2.401 04 (5/U)- 1 • 
(2.6) (3.1) 
R2 = .875 MAE <mean absolute error) = .270 
PRICE (p) 
P0 ' , , 
1 
I \ } .. 
P~ r• --t' --\\-~" .. 
Po 
3 
pO 
4 
S~U0 
19 
STOCKS-TO-USE RATIO (S/U) 
h = harvest quarter 
h + 1 a 1 quarter after harvest 
h + 2 • 2 quarters after harvest 
h + 3 a 3 quarters after harvest 
P = prtce per bushel of wheat 
~ • harvest quarter prtce tor a gtven stock-to-use ratio (5°/UO) 
~., • harvest + 1 quarter prtce tor a gtven stock-to-use ratio (5°/UO) 
~.2 • harvest + 2 quarter price tor a gtven stock-to-use ratio (5°/UO) 
~.2 • harvest + 3 quarter prtce tor a gtven stock-to-use ratto (5°/UO) 
SO/UO • a gtven stock-to-use ratto 
Ftgure 1. Relattonshtp Between Quarterly Prtce and Stocks-to-use Ratto 
20 
The sign of the coefficients on the stock-to-use ratios were positive 
and tended to diminish as the time from harvest increased. This met 
with the expectations of Westcott et al. (1984). 
To assess the predictive capabilities of their model, Westcott et 
al. (1984) forecasted quarterly price for the years 1982 and 1983. For 
1982 a mean absolute error (MAE) of 24.2 cents per bushel was obtained 
and for 1983 an MAE of 31.1 cents per bushel was obtained. This was felt 
to be acceptable performance for a wheat forecasting model although they 
noted that some problems with forecasting may have been caused by the 
1983 PIK program and the 1983 drought. 
Another publicly available source of commodity forecasting models 
is the many books and pamphlets published by futures traders and 
analysts. Schwager (1984) contributed to this body of information when 
he published the book A Complete Guide to the Futures Markets. While not 
explicitly creating and testing a wheat forecasting model, Schwager 
presented theoretical arguments for a general model form. Since this 
book represented a fairly new and available publication on wheat market 
models, it was chosen as a literature source that met the general cost­
availability framework discussed earlier. The following section will 
develop Schwager's (1984) general wheat model. 
The basic model proposed by Schwager is: 
(13) DP = a + b(D5/ES). 
Where DP is the average deflated cash wheat price for the period in 
question, a and b are parameters to be estimated by regression, and 
05/ES is a ratio of five period average disappearance of grain stocks to 
ending grain stocks. The five period moving average of grain stock 
21 
disappearance, 05, was used to normalize stocks since Schwager felt that 
this would be a more representative measure of the size of the market. 
A single period, D, could make the model unstable by making it prone to 
being affected by short period abnormalities that can occur in any 
market. It was suggested, however, that the length of the moving 
average on stock disappearance be varied until "best model fit" is 
obtained. 
Schwager viewed the general model (13) as a logical starting point 
for constructing price forecasting models of the grain markets. Once 
this basic model was tested, the analyst can then experiment with the 
addition. of other variables. Two potential right-hand side variables 
that were suggested are: (appropriately lagged) wheat-to-corn price 
ratios and trade dollar values. Schwager stated that some very 
impressive model fits (~ of .89 to .98) had been obtained using these 
methods, but did not explicitly show the actual models. 
There are many other wheat price forecasting models in 
publications. However, those reviewed by this author followed the 
general framework of Schwager (1984) and/or Westcott et al. (1984). All 
models had lagged wheat price or wheat-to-feed grain price ratios and 
either lagged or forecasted supply-disappearance variables on the right-
hand side. Therefore, the two wheat price models discussed above are 
felt by this author to be representative of the literature available. 
General Auto-regressive Integrated Moving 
Average Modeling Theory 
Box and Jenkins (1976) are generally considered the creators of a 
form of time series analysis that is referred to as autoregressive 
integrated moving 
defined as follows: 
CAR) lag, the d 
22 
average {ARIMACp,d,Q)) modeling. 
the p represents the order of the 
represents the number of times 
The Cp,d,q) is 
autoregressive 
the data were 
differenced, and the q represents the order of the moving average 
(abreviated MAl error term. (The Cp,d,q) will not be presented unless a 
specific model structure is being discussed.) In this approach to time 
series analysis the goal is generally prediction; therefore, little 
emphasis is placed on explanation. As a result, ARIMA modeling has a 
much more limited application than most forms of time series econometric 
modeling; econometric models are often as concerned with explanation as 
with prediction. 
ARIMA modeling is generally broken down into a four-fold iterative 
exercise. The four basic exercises are: (1) identification, (2) es­
timation, (3) diagnostic checking, and (4) forecasting. The first 
three steps are iterative. The fourth step is taken only when 
satisfactory results are obtained from steps 1 through 3. The rest of 
this section will discuss the characteristics that a data series need 
exhibit to be a candidate for ARIMA modeling, and will present a brief 
discussion of each of the steps involved in ARIMA modeling. Brevity was 
considered reasonable since ARIMA modeling is a well known and accepted 
process. For an in-depth discussion refer to Time Series Analysis: 
Forecasting and Control (Box and Jenkins, 1976). 
Candidate data processes for ARIMA models must have some basic 
characteristics. These characteristics are: (1) the data set must 
contain data that was measured in equally spaced, discrete time 
intervals (Box and Jenkins (1976) suggest at least 50 observations), 
I 
I 
' 
23 
(2) the mean of the data series must be constant through time, (3) the 
. variance of the data series must be constant through time, and (4) the 
autocorrelation function must be constant through time; autocorrelation 
must be a function of lag length only, i.e. relative position in the 
series cannot have any effect on autocorrelation. 
If a candidate data set satisfies all the preceding 
characteristics, then it is referred to as second order stationary (505) 
and is a good candidate for univariate, Box and Jenkins ARIMA. It a 
data set does not satisfy these characteristics, then the accepted 
methodology is to difference the series to try to obtain sos. A data 
series that cannot meet 50S criterion is not a candidate for ARIMA 
modeling. 
If a data set meets the requirements tor ARIMA modeling, the next 
step is the identification stage. Identification is the step in which 
one or more possible ARIMA models are chosen as candidates for building 
the forecasting model. Two graphical devices are used to measure 
correlations between observations within a single data series. These 
devices are called an estimated autocorrelation function (act) and an 
estimated partial autocorrelation function Cpacf). The estimated act 
and pact measure the statistical relationships within a data series and 
are helpful in giving a feel for the patterns available in the data. 
The estimated act and pact are then used as guides in choosing one 
or more ARIMA models that seem appropriate. Thus, the basic idea is 
that every ARIMA model has a theoretical act and pact associated with 
it. At this stage the theoretical acts and pacts are compared with the 
estimated acts and pacts in order to select a model whose theoretical 
24 
acfs and pacfs most closely match the estimated acfs and pacts. The 
data is not approached with a preconceived idea about what model to use, 
as in the case of econometric models; rather, the data is expected to 
"talk" through the estimated acfs and pacfs and ihereby reveal the model 
of choice. Models are only chosen tentatively at the identification 
stage; a tentative model will not be accepted as a final model unless 
it proves adequate in the estimation and diagnostic checking stages. 
Otherwise the identification stage must be rep~ated. 
The estimation stage is where precise estimates of the coefficients 
of the chosen model are obtained. This stage provides some warning 
signals about the adequacy of a model. In particular, the estimated 
coefficients must meet certain mathematical constraints (size and sign) 
or the tentative model is rejected. A model that 
constraints will not satisfy stationarity 
requirements. For a more detailed explanation of 
invertibility see Pankratz (1983). 
doesn't meet these 
and/or invertibility 
stationarity and/or 
The third stage of ARIMA modeling is the diagnostic checking stage. 
Box and Jenkins (1976) suggested some diagnostic checks to help 
determine if an estimated model is statistically adequate. This stage 
is mainly concerned with looking at the residuals in order to determine 
if only white noise remains. If a model is shown to be inadequate in 
this stage, then stage 1 (identification) must be returned to. 
The fourth and final step in ARJMA modeling is forecasting. 
Assuming that all the requirements of steps 1 through 3 are satisfied, 
the model is then used to derive forecasts. If the ARIMA model chosen 
is indeed the correct one, then forecasts made with this model are said 
25 
to be optimal. This means that no other univariate forecasts have a 
smaller mean-squared forecast error CMSE). 
Development of an Efficiency Test 
for the Wheat Futures Market 
The following section traces the general ideas and concepts behind 
the efficiency test that is undertaken by this study. All references to 
efficiency in this section refer to the Fama (1970) definition of 
efficiency. 
The market that is tested for efficiency in this study is the 
Chicago Board of Trade's wheat futures market. The contract tendered on 
the Chicago Board of Trade's wheat futures market is for number 2 soft 
red winter wheat deliverable upon contract expiration to any of several 
designated delivery points. One such point of delivery that is not 
subject to location premiums or discounts is Chicago, thereby making 
cash price for number 2 soft red winter wheat at Chicago a logical 
choice for a data series to be used in this study. 
The next step is to choose a time interval to forecast since the 
Chicago Board of Trade's wheat futures market is capable of making 
forward price predictions of any length less than 15 months. However, 
close examination of the relationship between the length of the price 
prediction (contract length) and the number· of predictions made 
(contracts traded) indicates that near term contracts (short length 
" predictions) experience the greatest trading volume. Since there are 
five contracts (December, March, May, July, and September) traded per 
given year, each contract spends approximately two and one-half months 
26 
being the near term contract. The closest any readily available, cash, 
number 2 soft red winter wheat data set could come to matching this 
prediction interval was in quarterly format. As a result, quarterly 
intervals were chosen to be the standard by which efficiency tests were 
made; a quarterly, cash price, number 2 soft red winter wheat data 
series was obtained for the period from the first quarter 1966 to the 
2nd quarter 1986. 
After selection of the prediction interval and data set, the next 
step becomes selection of the appropriate efficiency test. The 
efficiency tests used in this study closely follow the framework 
proposed . by Fama in 1970. 
The version of the Fama (1970) efficiency test that is undertaken 
requires the creation or selection of a standard (norm) with which to 
compare the price prediction capabilities of the market in question. 
Conclusions on market efficiency or, at least, conclusions about market 
efficiency relative to the model chosen for comparison, can then be 
reached. Logically, "simple" (easily constructed and utilized) models 
should be chosen first since an efficiency rejection by a "simple" model 
precludes the necessity of creating a more complex model. It must also 
be recognized that a Fama (1970) form rejection of efficiency represents 
only the necessary condition for general efficiency rejection. 
Therefore, since the sufficient condition for efficiency rejection 
requires that model cost be taken into account, the cost of creating and 
utilizing complex models often makes them fail sufficiency criterion. 
Perhaps the most simple model of a market proposed is that of a 
random walk; it takes minimal knowledge and time to test the hypothesis 
27 
that a data set is a random walk. If the data set does not follow a 
random walk, then this indicates that it may be possible to build a 
model or follow some other trading rule that will allow better 
predictions than those generated by the market. The general cash wheat 
random walk model is: 
(14) WPt: = a + 13WPt:-t · 
Where WPt:-t represents cash, number 2, soft red winter wheat price at 
Chicago in the (t-i)th quarter, a is an intercept parameter to be 
estimated, and 13 is a slope parameter to be estimated. 
The random walk model has 13 equal to one and a equal to whatever 
number best represents the market drift, i.e. a market with no drift 
would have a equal to zero, whereas a market with positive growth would 
have a greater than zero. Therefore, the hypothesis to be tested is 
that 13 
freedom 
= 1. 
(n 
The T test is the appropriate test with 
is the number of observations). A 
n-2 degrees 
rejection of 
of 
the 
hypothesis that 13 = 0 is a Fama (1970) weak form rejection of 
efficiency. 
If the wheat price series do not follow a random walk, then this 
indicates the possibility of building an ARIMA model to compete with the 
wheat futures market. A random walk model is an AR(l) process; 
therefore, the rejection of a random walk model poses the possibility of 
creating a model that has an AR(p) process with p>l. An ARIMA(p,d,q) 
model where the exact form is not ARIMA(l,O,O) indicates that current 
price does not "fully reflect" available information. If such a model 
succeeds in rejecting wheat futures market efficiency, then this would 
represent a Fama (1970) semi-strong rejection of market efficiency. 
28 
Models other than ARIMA can be used to serve as a norm for 
efficiency comparisons; any model or rule that allows for either actual 
price prediction or predicts direction of price change is a viable 
candidate for an efficiency test. Two other competing models were 
selected from the literature to serve as comparison norms in this study. 
The general form of and theory behind the models selected (model (11) 
and model (13)) are given in a previous section. Model selection is 
chosen over model creation to allow for tests of models that are 
currently in the literature. This is especially relevant in the case of 
model (11) since this model is one that the USDA advocates. The USDA is 
possibly the largest, most easily available source of commodity price 
predictions. Another benefit of model selection over model creation is 
that with model selection the right-hand side variables don't have to be 
derived and defended. 
The statistics that will be used for comparison between models of 
the wheat market and the wheat futures market are RMSE and bias. The 
selected statistic of comparison is RMSE since it effectively penalizes 
large prediction errors more than small prediction errors. This is 
important since it is the large errors in wheat price prediction that 
could more effectively lead to resource allocation problems. Bias is 
also chosen as a statistic of comparison to effectively rate how the 
wheat futures market fared against the other chosen models in the area 
of consistent resource allocation. A biased model or futures market 
will consistently misallocate resources through time~ Both bias and 
RMSE are commonly accepted measures tor tests such as these. 
! 
29 
The final empirical step taken in this study only occurred because 
one of the preceding models (ARIMA) succeeded in obtaining a Fama (19701 
semi-strong rejection of market efficiency. Since a Fama rejection of 
efficiency meets only the necessary condition for general market 
efficiency rejection, the sufficient condition for efficiency rejection 
must be examined. In order to meet sufficiency requirements for a 
rejection of 
enough returns 
market efficiency, a competing model must 
(risk adjusted) to cover the cost of 
generate 
building 
high 
and 
utilizing the competing model. Returns from trading the model that met 
the necessary criterion will be measured, the cost of building the model 
will be estimated, and the opportunity cost of money invested in the 
model will be figured at a 101 discount rate. However, the returns from 
speculating with a price predictive model need to be adjusted for risk 
before comparing them to returns from other investments. Since risk 
adjustment is a function of personal preference, no attempt will be made 
to adjust returns for risk. Individuals that review this study will 
have to choose a method of adjusting returns to reflect their risk 
preferences and thereby reach a conclusion as to whether the sufficient 
condition for wheat market efficiency rejection is met. 
Data Availability and Requirements 
Quarterly measures of the following variables from 1966 to 1986 
were required: number 2 Chicago cash price for soft red winter wheat, 
producer price index (PPI}, total grain usage, ending grain stocks, 
trade weighted dollar values, and cash corn prices. All the data were 
readily available from the following government publications: Wheat 
30 
Outlook and Situation Report, Feed Outlook and Situation Report, 
Agricultural Outlook, and The Economic Report of The President. 
Efficiency tests require that an accounting of the costs of data 
gathering be kept in mind; however. the data required for this study did 
not represent a problem in this area. All the data sources are easily 
obtained from libraries or can be ordered on an annual basis for fees 
that total less that $100. 
31 
CHAPTER 3 
EMPIRICAL RESULTS 
The previous chapters presented the theoretical basis for this 
study. This chapter summarizes the actual empirical results. The 
estimation of the models used in this study is completed using the 
statistical package DYNREG (Burt et al., 1986). 
This chapter is divided into five sections. The first ~ection 
presents the results of fitting ARIMA models to the cash wheat market. 
The second section gives the results obtained from efficiency testing 
with model (11). The third section gives the results obtained from 
efficiency testing with model (15). The fourth section provides the 
results acquired from modeling the producer price index. The fifth 
section presents the costs of utilizing and the potential returns from 
speculating with the best competing model. 
Soft Red Winter Wheat ARIMA Models 
Random Walk Model Results 
An ARIMA modeling process begins with a visual examination of the 
candidate data series to check for obvious problems that the series may 
exhibit regarding 50S; visual examination (see Figure 2) of both the 
nominal and real cash wheat series raises some real questions as to 
whether the series has constant mean and/or constant variance. The 
nominal data series appears to exhibit a slight growth rate, and both 
11 
10 
9 
+ NOMINAL WHEAT PRICE 
B • REAL WHEAT PRICE <1985•100> 
0 7 
0 
L 8 L w N A 
R 5 s 
4 
3 
:J ~~~i~l~i~i~IMi~i~lrrtrjTITiTITITiTITITITI~j~l~i~l~i,l,l,i~l~i~jrriTITITITITITITITI,j~i~i~l~iMI~IrriTITITjTITITITITITITI~ITITjTITI~I,i,i,l~i~i~i~J~i~lrrtriTITITiTITITjTITITITI~iTITI~i~l~j 
0 10 20 30 40 50 60 70 eo 90 
QUARTERS C1966COTR1>-1986COTR2>l 
Figure 2. Nominal and Real Cash Soft Red Winter Wheat 
I" 
33 
the nominal and real data series appear to exhibit some structural 
variance changes in the quarters of 1973-1974 (specifically the 4th 
quarter of 1973 and the first two quarters of 1974}. At this point it 
became necessary to choose to work with either the nominal or real price 
series. Since the futures market's price predictions are made on a 
nominal basis, the nominal data series were chosen as the appropriate 
series to work with to create the ARIMA model. The nominal series were 
then split in half (41 quarters per half} in order to compare the mean 
and variance of the two halves. The mean of the first half of the data 
set equals $2.39, whereas the mean of the second half of the series 
equals $3.41. The variance of the first half of the data set is equal 
to $1.64 whereas the variance of the second half the the data set equals 
$0.35. ' 
The mean and variance statistics indicate a problem with 505. Box 
and Jenkins (1976) suggest differencing to deal with problems of this 
nature, so this is initially the approach taken. The differenced 
series became constant mean; however, the constant variance problem 
caused by the 1973-1974 quarters did not improve. In fact, as the 
degree of differencing increased, the constant variance problem actually 
worsened. At this point either a time series approach other than ARIMA 
or a dummying of the problem quarters in 1973 and 1974 became necessary. 
Visual examination of a quarterly price chart for wheat from 1900 
through 1988 indicates that ~he large variance appearing in the 1973-
1974 time frame is an anomaly in this longer (352 quarter) series. 
Historically, there exists an explanation for the violent price changes 
of this period. In 1972 the Commodity Credit Corporation (CCC}, eager 
I 
34 
to unload grain stocks in government storage, struck a bargain with 
drought stricken Russia which completely emptied the CCC stocks of grain 
(400 million bushels) by 1974. Also, in this time frame, the 
Organization of 
bringing 
Petroleum Exporting Countries 
an end to the era of cheap 
(OPEC) 
energy. 
embargoed 
Both 
oi I, 
these thereby 
factors contributed strongly to the tremendous price variance 
experienced in this time period. However, it can be inferred from the 
1900-1988 quarterly wheat chart (indicating the 1973-1974 time frame as 
an anomaly) that both the OPEC oil embargo and the Russian wheat deal 
were uncommon occurrences and unlikely to reoccur. 
Given, then, that the price variance of the fourth quarter of 1973 
and of the first and second quarters of 1974 can be described as an 
abnormality, it seems reasonable and prudent to take the dummying 
approach to stationarity. A zero/one dummy is regressed as a right-hand 
side variable where the fourth quarter of 1973 and the first and second 
quarter of 1974 are dummied out. The dummy variable is included in the 
difference equation (distributed lag effects) to allow for a gradual 
timing out of the 1973-1974 variance effects since this better 
represents the gradual disappearance of the real world market influences 
occurring during this time frame. The zero/one dummy should effectively 
compensate for the variance problems of the 1973-1974 period, thereby 
making an ARIMA representation of this data series possible (OYNREG, a 
nonlinear least squares algorithm for distributed lag models, is capable 
of dealing with the slight drift in the data series <Burt et al., 
1986). 
35 
Because seasonality exists in the quarterly wheat data series, one 
other modification is made in the basic ARIMA process. The approach 
taken to this problem is to dummy out the seasonal component. This is a 
quite straightforward and well accepted procedure for seasonal models 
(Johnston, 1984). Zero/one dummies are used for the second, third, and 
fourth quarter of each year which results in the intercept coefficient 
carrying any seasonality information that is present in the first 
quarter. 
The first ARIMA(p,d,q,J model to be considered is the ARIMA(l,O,O) 
model (random walk model). Tests of whether markets follow random walk 
models are Fama (1970) weak form efficiency tests. Model (14) presented 
the general form (ARIMA(1,0,0J) of a wheat market random walk model. 
The sos requirements resulted in the general form having to be modified 
slightly to deal with the seasonality and variance problems (505 
problems) of our particular data set, i.e. seasonal dummies and a dummy 
for the fourth quarter of 1973 through the first two quarters of 1974 
were added as previously discussed. The result of these modifications 
on the general random walk model is: 
(15) PWt. =a+ /i 1 02 + /i2 03 + /i3 04 + 
/i4 073 + cx:PWt._ 1 + Ut.. 
with ut. = Et.. 
Where PWt.-~ is the cash price of number 2 soft red winter wheat in the 
(t-i)th quarter, 02-04 are the seasonal dummy variables for the second, 
third, and fourth quarters of the year respectively, 073 is a dummy 
variable for the fourth quarter 1973 through second quarter 1974 time 
period, and Ut. is the error structure <MA(O)J. 
36 
To be a random walk with a drift, the coefficient on the PWt_ 1 
term, oc, has to be equal to one (the other coefficients will pick up the 
drift effects); the null hypothesis tested is that~ equals 1 versus the 
alternative hypothesis that~ is not equal to 1. The appropriate test 
is the T test with n-6 degrees of freedom (n is the number of 
observations). 
The empirical results of estimating model (15) are: 
(16) PWt = .37572 - .18374 02 - .0010047 03 + .097382 04 + 
(2.98) (2.26) (1.07) (1.21) 
1.1155 073 + .8638 PWt-1 + Ut. 
(4.65) (21.35) 
with ut = Et. 
lf2 = . 88. 
The null hypothesis that model (16) represents a random walk is 
tested at the 1 percent level of confidence. The calculated T-statistic 
to test the significance of the estimated parameter of the lagged price 
of wheat CPW> regressor is: 
Tc.a1.7b) = 3.36. 
At the 1 percent level of significance the hypothesis that the cash 
wheat market follows a random walk is rejected. 
The rejection of the ARIMAC1,0,0) model (random walk with a drift) 
of the cash wheat market introduces the possibility of other 
ARIMA{p,d,q) forms better modeling this market. However, before leaving 
this section on random walk models, it is pertinent that the so-called 
"simple" random walk model be discussed since the "simple" random walk 
model of futures markets is quite popular in the efficiency literature. 
37 
The general model that represents the "simple" random walk is: 
( 17) PWt: = adj ( PWt:-t ) + Ut:. 
Where PWt-t is wheat price in the (t-i)th quarter, and the (adj) prefix 
represents adjustments made for predicted inflation. 
Model (17) is used to forward predict wheat price (the inflation 
adjustments, (adj), are acquired by using the ARIMA(l,O,O) PPI model 
discussed in a following section to obtain one step ahead forecasts of 
the PPI which are then used to adjust price). Table 1 presents the 
results of the forward price predictions of the simple random walk model 
(from first quarter 1982 through second quarter 1986) and the calculated 
RMSE and bias statistics. 
Table 1. Price Predictions with a Random Walk Model 
Time Period Cash Price Prediction Residual 
1982 I 3.59 3.70 0.11 
1982 II 3.31 3.54 0.23 
1982 I II 3.18 3.35 0.17 
1982 IV 3.23 3.12 -0.11 
1983 I 3.36 3.14 -0.22 
1983 II 3.53 3.34 -0.19 
1983 II I 3.62 3.54 -0.08 
1983 IV 3.55 3.72 0.17 
1984 I 3.57 3.64 0.07 
1984 II 3.51 3.79 0.28 
1984 II I 3.47 3.65 0.18 
1984 IV 3.49 3.57 0.08 
I 1985 I 3.58 3.58 -0.00 
1985 II 3.27 3.60 0.33 
1985 II I 2.83 3.22 0.39 
1985 IV 3.46 2.70 -0.76 
1986 I 3.40 3.45 0.05 
1986 II 2.52 3.32 0.80 
RMSE = .3193952 
Bias = 8.220535E-02 
38 
When compared to predictions made by the actual Chicago Board of 
Trade's wheat futures market, the "simple" random walk models 
predictions don't appear to fare too badly. In fact, the random walk 
model's predictions had a 32 percent lower bias while only measuring 11 
percent higher RMSE. Table 2 presents the wheat futures markets 
predictions. 
Graphically, the "simple" random walk model appears to consistently 
lag behind the market by a small amount (see Figure 3). Since cash wheat 
price in the time frame examined had about the same amount of up and 
3.8 
3. 7 
3. 6 
3. 5 
3."' 
3. 3 
3. 2 
D 3. 1 
0 3. o I L 
L 2. 9 
A 
R 2. B + NOMINAL WHEAT PRICE 
s 2. 7 • RANDOM WALK FORECASTED PRICE 
2. 6 
2.5 
2."' 
2. 3 
2.2 j 
2. 1 
2. 01 
I 
2 3 5 6 7 B 9 10 11 12 13 15 1e 17 18 
QUARTERS Cl9B2<CTR1>-19B6<CTR2>l 
Figure 3. Rftndom Walk Model's Forecast versus Cash Price· 
40 
down trends, the lower bias of the "simple" random walk model can be 
explained. The random walk model tends to underestimate an up-trending 
market and overestimate a down-trending market so, if a time frame where 
the up-trending period is about equal to the down-trending period is 
examined, the bias of the random walk model's predictions will be 
small. The futures market's price predictions didn't appear to lag 
behind as consistently as the random walk model's price predictions. 
However, the futures market's price 
extremely large error (see Figure 4). 
predictions had an occasional 
Since this study did not establish which statistic of comparison is 
of greater value, any inferences made as to which model is "better" are 
left to the reader. When comparing these two models it must be kept in 
mind that only a short prediction period was analyzed, and that there is 
a definite cost savings in using the futures market to predict price 
since this eliminates modeling the PPI. 
ARIMA(3,0,3) Model Results 
Since the ARIMA(l,O,O) model form of the wheat market is rejected, 
the next step is to identify other ARIMA(p,d,q) model forms that may be 
more representative of the wheat market. Figures 5 and 6 present the 
acf and the pact which are the main toots for identification. The act 
rapidly tails off and the pact cuts off at lag= 3. Thus, at the 
identification stage, a preliminary model of ARIMA(3,0,0) is indicated. 
However, this model is rejected at the diagnostic stage because of 
autocorrelation problems in the residuals. The identification step is 
returned to, and thus the procedure iterates. 
4.2~ 4. 1 
4. 0 
3. 91 3. 9 
3. 7 
3. 4 :~ :1'"' 
0 3. 3 
0 
L 3. 21 
L 3. 1 
A 
: :: :j 
2. 71 
2. 61 
2.5 
2. 4 
2. 3 
2. 2 
2. 1 
+ NOMINAL WHEAT PRICE 
9 FUTURES MARKET FORECASTED PRICE 
2.0\-~~--~-~,_~_,~·r~~--.-~-.~--.-~.--r-.--.-~.--.-.--r-~-r~~r-r-,--r~-.~ 
2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 17 18 
QUARTERS [1982<CTR1>-1986CCTR2>l 
F1gure 4. Wheat Futures Market's Forecast versus Cash Pr1ce 
42 
LAG COVARIANCE CORRELATION -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 
0 1.85037 1.00000 
1 1.57016 0.84857 
2 1.23148 0.66553 
3 1.05088 0.56793 
4 0.878363 0.47470 
5 0.591566 0.31970 
6 0.35232 0.19041 
7 0.219312 0.11852 
8 0.147348 0.07963 
9 0.00366617 0.00198 
10 -0.129182 -0.06981 
11 -0.21352 -0.11539 
12 -0.294936 -0.15939 
13 -0.38413 -0.20760 
14 -0.445252 -0.24063 
15 -0.444216 -0.24007 
16 -0.426661 -0.23058 
17 -0.423582 -0.22892 
18 -0.391886 -0.21179 
19 -0.317129 -0.17139 
20 -0.272567 -0.14730 
21 -0.249191 -0.13467 
22 -0.184567 -0.09975 
23 -0.109745 -0.05931 
24 -0.0847079 -0.04578 
25 -0.0877323 -0.04741 
26 -0.0521646 -0.02819 
27 -.00209514 -0.00113 
28 0.0363057 0.01962 
29 0.0242609 0.01311 
30 -0.0328679 -0.01776 
31 -0.0586484 -0.03170 
32 -0.0612425 -0.03310 
33 -0.10677 -0.05770 
34 -0.17065 -0.09222 
35 -0.191801 -0.10366 
36 -0.198048 -0.10703 
'.'Marks Two Standard Errors 
* 
** 
*** 
**** 
***** 
***** 
***** 
***** 
I********************: 
:***************** 
l************* 
l*********** 
l********* 
l****** 
l**** 
l** 
l** 
****· 
***l 
***l 
***: 
**l 
*l 
*' 
* 
* 
* 
* 
* 
** 
**l 
**l 
Figure 5. Autocorrelation Function (ACF) for Cash Wheat 
43 
LAG CORRELATION -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 
1 0.84857 I l***************** I . 
2 -0.19483 I *****l I 
3 0.21715 I I**** I 
4 -0.12950 I 
·***l I 
5 -0.21590 I ****l I 
6 0.03731 I l* I 
7 -0.01012 
8 0.07198 I I* I 
9 -0.15443 I 
·*** I 
10 0.00254 
11 -0.08264 I 
. ** I 
12 -0.08011 I 
. ** I 
13 0.00650 
14 -0.04542 I * I 
15 0.06273 I l* I 
16 -0.04855 I *l I . 
17 -0.01333 
18 0.01769 
19 0.00842 
20 -0.03990 I *l I . 
21 -0.00482 
22 0.06038 I l* I . 
23 -0.03827 I *l I . 
24 -0.03405 I *l I 
25 -0.03357 I *l I 
26 0.02206 
27 -0.00280 
28 0.05123 I l* I . 
29 -0.08317 I . **l I 
30 -0.12814 I 
·***l I 
31 0.03920 I l* I . 
32 -0.02338 
33 -0.02867 I *l I . 
34 -0.03198 I *' I 
35 0.00039 
36 -0.04876 I *l I . 
' ' Marks Two Standard Errors 
Figure 6. Partial Autocorrelation Function (PACF) tor Cash Wheat 
44 
The ARIMA(3,0,3) form is accepted as satisfactory for the following 
reasons: (1) the estimation stage ARIMA criterion appear fulfilled 
since the coefficients on the AR terms sum to less than one (Pankratz, 
1983). and (2) the diagnostic stage is fulfilled because the 
autocorrelation test on the residuals can't reject the hypothesis that 
the residuals are uncorrelated. The test used on the residuals is a 
statistic whose approximate distribution is chi-squared under the null 
hypothesis that the residual serjes is white noise (Pankratz, 1983). 
The exact form of the test used on the residuals is: 
k 
a* = n c n + 2 > t r2 c j > 1 c n - j > j=l 
Where n is the number of observations, r( j) is the estimated 
autocorrelation at lag j, and k can be any positive integer. Table 3 
presents the results of letting k = 6, 12, 18, and 24. 
Table 3. Autocorrelation Check of Residuals 
(18) 
To Chi 
Lag Square OF· Prob <------AUTOCORRELATIONS----------------> 
6 
12 
18 
24 
0.00 0 
5.43 5 
8.14 11 
11.49 17 
0.000 0.020 0.029 -0.031 
0.366 -0.133 0.045 -0.045 
0.701 -0.079 -0.128 -0.015 
0.830 0.035 0.050 0.097 
0.108 
0.013 
-0.030 
0.068 
-0.126 0.061 
0.031 -0.059 
0.051 0.019 
0.053 0.093 
The general form of the final ARIMA(3,0,3) is: 
PWt = a + 3'102 + 3'203 + 3'3 03 + 3'4 073 + 
~1 PWt-1 +~2 PW1::-2 + ~t P~-:s + U1::. 
with Ut = Et - }.1 Et-1 - X2 Et-2 - X:s Et-:s · 
45 
Where PWt-i is the cash price of wheat in the (t-i)th quarter, 02-04 are 
seasonal dummy variables (~contains the information for 01), 073 is a 
dummy variable for the fourth quarter of 1973 through the second quarter 
of 1974, and Ut represents the error process (MA(3)). The coefficients 
to be estimated by regression are~. r, ~. and A. 
A comparison of the price predictions made by the ARIMA(3,0,3) 
model developed and the wheat futures market's price predictions 
constitutes a Fama (1970) semi-strong test for market efficiency. The 
null hypothesis tested is that the wheat futures is efficient, i.e. the 
wheat futures market has the lowest bias and RMSE forward price 
forecaster. The alternative hypothesis is that the wheat futures market 
is not the lowest RMSE and bias forward price predictor. 
The general ARIMA(3,0,3) model (18) is estimated over the first 
quarter 1966 through second quarter 1986 time frame and is then used to 
recursively forecast the last 18 quarters of this time period. Whi 1 e 
recursively forecasting, the model structure is observed to see if model 
structure updating would improve fit since structural updating for best 
fit is allowable in ARIMA modeling, i.e. this study uses an ARIMA model 
to forecast price and not to explain structural relationships, thereby 
making model updating through time to best fit a necessity. The choice 
of changing ARIMA model structure through time is also consistent with 
real world behavior since one would expect ARIMA model users to update 
their model's structure to best fit through time. The empirical results 
of estimating model (18) over the entire period are: 
46 
( 1 9 ) PWt = . 4 7 5 3 4 
(2.27) 
.000000127 02 -.00000000442 03 + .00365 04 + 
(3.98) (2.39) (1.07) 
2.3416 073 + .37671 PWt_ 1 - .28826 PWt_2 + .71819 PWt-3 + Ut. 
(9.02) (6.68) (5.00) (15.55) 
With Ut = Et - . 50331 Et-1 
(4.02) 
- 1.0459 Et-2 
(11. 88) 
. 381 71 Et-3. 
( 2. 85) 
~ = .94. 
Where the variables are as defined for model (18). 
The coefficients that resulted from this estimation are all 
statistically significant with the exception of the coefficient on 04. 
Since this is a seasonal model, 04 is kept in as a regressor. The 
coefficient estimates and error structure satisfies the ARIMA criteria 
for a forecasting model, i.e. the coefficients on the AR terms sum to 
Jess than one. This suggests stationarity; therefore, the hypothesis 
that the error structure is uncorrelated can't be rejected (see Table 3 
preceding). 
Model (19) is then used to recursively forecast 18 quarters. The 
empirical results of the shortest model (first quarter 1966 through 
fourth quarter 1981) are: 
(22) PWt = .43498 - .000000129 02 - .00000000194 03 + .003885 04 + 
(2.66) (3.20) (.340) (.644) 
2.411 073 + .37073 PWt-1 - .28518 PWt-2 + .69436 PWt-3 + Ut, 
(8.19) (4.55) (3.06) (9.08) 
with Ut=Et- . 48960 Et-1 -
( 1 • 90) 
1.7131 
( 6. 81 ) 
~ = .98. 
Et-2 - .36785 
( 1 • 40) 
Where the variables are as defined for model (18). 
Et-3 • 
The coefficients obtained from this estimation are all reasonably 
significant with the exception of the coefficients on 03, 04, and Et_3 • 
47 
The seasonal dummies, 03 and D4, are left in since this is a seasonal 
model and, while removal of the third order MA lag would be permissible 
in this situation, doing so proved detrimental to model fit. Since the 
coefficients on the right-hand side variables appeared to be fairly 
stable through time, and the model structure did not require updating 
through time, the indications are that this model fits this time frame 
f a i r 1 y we 1 1 . 
Forecasts obtained from using the ARIMA£3,0,3) model to one step 
ahead predict, along with the summary statistics RMSE and bias, are 
presented in Table 4. The ARIMA(3,0,3) model's price predictions had a 
62 percent smaller RMSE and a 68.5 percent smaller bias than the wheat 
futures market's price predictions for the first quarter 1982 through 
second quarter 1986 time frame. This constitutes a Fama (1970) semi­
strong rejection of wheat futures market efficiency. 
The ARIMA£3,0,3) model's forecasts do appear to lag the actual 
market price during trends, as did the random walk; however, the size of 
the lags are quite small, thereby explaining the small RMSE of this 
mode 1 (see Figure ,7). Other than this s 1 i ght 1 agg i ng prob 1 em, the 
results of using the ARIMA(3,0,3) model for forecasting are quite good. 
Caution needs to be taken when interpreting these results as they relate 
to the quality of the ARIMA(3,0,3) model as a forecaster of wheat prices 
over longer or other time frames since this model was fit for this time 
period and may not perform as well in other time periods. 
A discussion of the potential incremental returns from speculating 
with this model will be presented in the final section of this chapter. 
48 
Table 4. Price Predictions with an ARIMA(3,0,3) Model 
Time Period Cash Price Prediction Residual 
1982 I 3.59 3.57 -0.02 
1982 II 3.31 3.36 0.05 
1982 III 3.18 3.24 0.06 
1982 IV 3.23 3.16 -0.07 
1983 I 3.36 3.24 -0.12 
1983 II 3.53 3.36 -0.17 
1983 III 3.62 3.54 -0.08 
1983 IV 3.55 3.54 -0.01 
1984 I 3.57 3.52 -0.05 
1984 II 3.51 3.41 -0.10 
1984 II I 3.47 3.43 -0.04 
1984 IV 3.49 3.47 -0.02 
1985 I 3.58 3.49 -0.09 
1985 II 3.27 3.25 -0.02 
1985 II I 2.83 3.01 0.18 
1985 IV 3.46 3.24 -0.22 
1986 I 3.40 3.30 -0.10 
1986 II 2.52 2. 72 0.20 
RMSE = .1092907 
Bias = -3.444443E-02 
3. 2 
3. 1 
D 3. 0 
0 
L 2. 9 
L 
A 2. 9 + NOMINAL WHEAT PRICE Jl, 
R "' s 2. 7 • ARMA <3. 3> FORECASTED PRICE 
2. 6 
2. 5 
2." 
2. "l . 2 
2. I 
~ 2. 0 i I 
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 
QUARTERS C1982CCJTR1>-1986<CJTR2>J 
Ftgure 7. ARIMA(3,0,3) Model's Forecast versus Cash Prtce 
I 
f, 
··1 t 
50 
USDA Model Results 
The first structural model that this study examined is based upon 
the genera 1 USDA mode 1 (11 ) . The term "based upon" means that the same 
right-hand side variables as those found in model (11) are present in 
the model that is used for the efficiency test. However, lag lengths on 
the right-hand side variables and error structure are adjusted to obtain 
best fit. This is justifiable because the prediction periods and the 
data series time frame used in this study are different from those used 
by the USDA studies. Any general postulated cause/effect relationships 
proposed by the general USDA model (11) will be unaffected by these 
adjustments; only the lead/lag time relationships and error structure 
will change (changes are limited to those which improved model fit). 
The changes made resulted in the following general model form (referred 
to hereafter as the USDA model): 
( 21 ) PWt 
with 
4 
=a+ /3PWt_1 +.:E C1 D1 (U/S)t_1 J=1 
Ut = Et - A1 Et-1 · 
+ Ut, 
Where PWt_1 is the cash price of wheat in the (t-i)th time period, D1 is 
a dummy variable representing the (i)th quarter (i=1 for the January 
through March quarter, i=2 for the April through June quarter, etc.), 
(U/S)t-1 is the quarterly use-to-wheat ending stocks ratio lagged 
time period, and Ut is the error structure (MA(1)). 
The first step taken with this model is an attempt to match the 
USDA's results by estimating the model over the same time period as the 
one used by Westcott et al (1984), i.e. 1971 through 1983. An exact 
51 
match is not expected since Westcott et al. (1984) did not identify 
exactly what wheat series they were working with and it is unlikely that 
it was number 2 soft red winter wheat nor; did they publish exactly what 
error structure is used in their model. The model form obtained is: 
(22) PWt = .619 + .400 PWt- 1 + 3.937 D1 (U/Slt-1 + 6.836 D2 (U/Slt-1 + (4.30) 
with 
(2.74) (2.74) (2.44) 
7.289 D3 (U/S)t-1 + (3.90) 
6.409 D4CU/S)t-1 + Ut, 
( 2. 87) 
Ut = Et - . 7 31 Et -1 , 
(5.17) 
1(2 = . 85. 
While the coefficients of model (22) don't exactly match those of the 
USDA model (12), the coefficients of model (22) are significant and the 
fit is reasonable for a structural model, thereby justifying the 
relationships proposed by Westcott et al. (1984) for this time frame. 
A comparison of the price predictions made by USDA model (21) and 
price predictions made by the wheat futures market constitutes a Fama 
(1970) semi-strong test of market efficiency. The null hypothesis is 
that the wheat futures market is efficient, i.e. the lowest RMSE and 
bias forward price prediction available is made by the wheat futures 
market. The alternative hypothesis is that the wheat futures market is 
not efficient, i.e. the lowest RMSE and bias forward price predictor is 
not the wheat futures market. 
USDA model (21) is estimated over the first quarter 1966 through 
2nd quarter 1986 time frame and then used to recursively forecast 18 
quarters in order to obtain forward price predictions (real values). 
Since these predictions are in real values they have to be changed, 
52 
using the predicted PPI, to nominal values. As this model is based uoon 
proposed relationships among variables, no structural updating through 
time is considered. The empirical results of estimating model (21) are: 
(23) PWt = .68055- .11830 Dl(U/S)t- 1 + 1.7466 D2(U/S)t_ 1 + (1.90) (.1387) (2.248) 
1.5797 03(U/5Jt_ 1 + .77304 D4(U/S)t_ 1 + .75023 PWt_ 1 + Ut, (1.75) (.655) (7.87) 
with Ut = Et - . 46252 Et-1 , 
(3.94) 
R2 = .82. 
Where the variables are as defined for model (21). 
The coefficients obtained from estimating this model are very 
disappointing. Only two of the right hand-side variables, PW t- 1 and 
D2CU/S)t_ 1 , have coefficients that are statistically significant. The 
low significance of the coefficients is reflected in the marginal model 
fit as defined by the R2 statistic. Clearly the extended time frame of 
first quarter 1966 through second quarter 1986 is not modeled as well by 
( 
this structural model as is the shorter time frame of first quarter 1971 
through first quarter 1983. This indicates that the relationships 
(model (21)) proposed by Westcott et al. (1984) may be a function of the 
period of time for which the market is examined. However, since this 
model is one that USDA publications present as representative of the 
wheat market, it is used to forecast wheat price. Table 5 presents the 
results of this forecast (predictions have been converted to nominal 
va I ues). 
53 
Table 5. Price Predictions with Model (23) 
Time Period Cash Price Prediction Residual 
1982 I 3.59 3.72 0.13 
1982 II 3.31 3.26 -0.05 
1982 I I I 3.18 3.86 0.68 
1982 IV 3.23 3.39 0.16 
1983 I 3.36 3.25 -0.11 
1983 II 3.53 3.23 -0.30 
1983 III 3.62 3.96 0.34 
1983 IV 3.55 3.84 0.29 
1984 I 3.57 3.49 -0.08 
1984 II 3.51 3.41 -0.10 
1984 II I 3.47 3.97 0.50 
1984 IV 3.49 3.90 0.41 
1985 I 3.58 3.39 -0.19 
1985 II 3.27 3.52 0.25 
1985 I I I 2.83 3.39 0.56 
1985 IV 3.46 3.05 -0.41 
1986 I 3.40 3.58 0.18 
1986 II 2.52 3.17 0.65 
RMSE = .3559516 
Bias = .1621556 
Model (23)'s price predictions have a 24 percent larger RMSE and a 
35 percent larger bias than the wheat futures market's price 
predictions; therefore, this model cannot reject the null hypothesis 
that the wheat futures market is efficient. Examination of the price 
I - predictions made by model (23) reveal large swings in the predicted 
price, thereby indicating model instability (see Figure 8). While this 
model may have adequately explained the first quarter 1971 through first 
quarter 1983 time frame, it certainly can't be advocated tor the first 
quarter 1966 through second quarter 1986 time frame. 
"'· 0 
3. D 
3.8 
3. 7 
3. 6 
3.5 
3."' 
3. 3 
0 3. 2 
0 L 3. 1 
L 3.0 
A 2. D 
R 
s 2.8 
2.7 
+ NOMINAL WHEAT PRICE 
• USDA MODEL FORECASTED PRICE 
QUARTERS C1982CQTR1>-1986CQTR2>l 
Figure B. USDA Hodel's Forecast versus Cash Price 
U1 
.. 
55 
Market Trader's Model Resul~s 
The next structural model is "based upon• model (13). The term 
"based upon• is· defined as discussed earlier. The exact model form 
obtained after adjustments is (referred to hereafter as the market 
trader's model): 
(24) PWt = a + /102 + /103 + /104 + /1073 + CX:1 (U4/S lt- 1 + 
CC::z(U4/S) + a1 (PW/PC>t- 1 + Ut, 
With Ut = Et - A1 Et- 1 - A2 Et_2 - A3 Et-::s. 
Where PWt is the price of wheat in time period t, a is the intercept 
term (contains ~he seasonal effects of quarter 1), 
I 
01 is a seasonal 
dummy representing the (i)th quarter (i=1 represents January through 
March, i=2 repres~nts April through June, etc.), 073 is a dummy variable 
tor the 1973 through 1974 time frame, (U4/S)t_ 1 is a variable 
representing the ratio in time period t-1 of the tour quarter moving 
average total wh~at use to total wheat ending stocks , (PW/PC>t-l is a 
variable representing the ratio in time period t-1 of cash white wheat 
to cash corn (corn and wheat price are deflated by the PPI), and ut 
represents the error structure(MA£3)). 
A comparison of the results of price predicting with market 
trader's model (24) and price predicting with the wheat futures market 
represents a Fama (1970) semi-strong test of market efficiency. Again, 
the null hypothesis is that the wheat futures market is efficient, i.e. 
the wheat futures market has the smallest RMSE and bias price forecaster 
versus the alternative hypothesis that the wheat market is inefficient, 
i.e. not the smallest RMSE and bias price forecaster. 
56 
Market trader's model (24) is estimated over the first quarter 1966 
.through second quarter 1986 time frame and then used to recursively 
forecast 18 quarters in order to obtain real price predictions. Again, 
these real price predictions are converted to nominal values using the 
predicted PPI values. Structural updating over time isn't considered 
for this model since it was designed t~ represent a relationship among 
variables. The empirical results of estimating this model are: 
(25) PWt = 1.7231- .39668 02- .58775 03 -.056751 04 + 4.0399 073 + 
(3.05) (2.65) (2.66) (.247) (9.18) 
1.7048 (U4/S)t_1 + 1.3028 (U4/S)t_2 +.99146 (PW/PC>t-1 + Ut, (4.01) (3.06) (2.70) 
with Ut = Et - . 44048 Et_1 -(3.36) 
~ = .90. 
. 33002 Et-2, 
(2.70) 
Where the variables are as defined for model (24). 
The coefficients on this model are all significant with the 
exception of the coefficient on seasonal dummy 04. This structural 
model appears to be much more structurally sound than the previous 
structural model (model (23)); model (25) fits this wheat data set and 
time frame relatively well as is indicated by the~ statistic, thereby 
suggesting that the variable relationships proposed by Schwager (1984) 
are fairly sound, at least for the period examined by this study. Table 
6 presents the one step ahead forecasts obtained by recursively 
forecasting with model (25) and then converting the real price values to 
nominal values. The summary statistics, RMSE and bias, are also 
presented in Table 6. 
57 
Table 6. Price Predictions with the Market Trader's Model 
Time Period Cash Price Prediction Residual 
1982 I 3.59 3.98 0.39 
1982 II 3.31 3.63 0.32 
1982 III 3.18 3.67 0.49 
1982 IV 3.23 3.71 0.48 
1983 I 3.36 3.50 0.14 
1983 II 3.53 3.35 -0.18 
1983 III 3.62 3.59 -0.03 
1983 IV 3.55 3.96 0.41 
1984 I 3.57 3.64 0.07 
1984 II 3.51 3.57 0.06 
1984 III 3.47 3.64 0.17 
1984 IV 3.49 3.96 0.47 
1985 I 3.58 3.87 0.29 
1985 II 3.27 3.60 0.33 
1985 I II 2.83 3.43 0.60 
1985 IV 3.46 3.28 -0.18 
1986 I 3.40 3.67 0.27 
1986 II 2.52 3.28 0.76 
RMSE = .3617189 
Bias = .2686888 
Model (25)'s price predictions have a 28 percent larger RMSE and a 
123 percent larger bias than price predictions made by the wheat futures 
market. Model (25l's performance is not good enough to reject the 
hypothesis that the wheat futures market is efficient. Model (25), the 
market trader's model, is by far the worst biased model of the group 
examined since it consistently overestimated market wheat price (see 
Figure 9). In fact, out of 18 quarters of price predictions, model (25) 
only underestimated market price three times. Clearly, model (25) isn't 
a good choice for use as a price prediction model. 
4.0~ 
3.9 
' 
3. e 1 
3. 7 
3. s 
3. 5 
3. 4 
3. 3 
D 3.2 
0 
L 3. 1 
L 3.0 
A 
R 2. 9 
s 2. 9 
2. 7 
2. 6 
2.5 
2. 4 
2. 3 
2.2 
2. 1 
+ NOMINAL WHEAT PRICE 
• FUTURES MODEL FORECASTED PRICE 
2.0 ~,-,--r-.~-.~r-r-~,-~-r~-.~r-r-~~,-~-r-r~~--r-r-~,-~-r-r-r~-T 
2 3 4 5 s 7 e 9 10 11 12 13 14 15 16 17 19 
QUARTERS [1992<CTR1>-198S<CTR2>l 
Figure 9. Market Traders Hodel's Forecast versus Cash Price 
Ul 
to 
59 
Predicting the PPI 
An ARIMA approach is taken to build a model that would yield one 
step ahead forecast of the PPI. The actual PPI data series used to 
deflate the price variables in the structural models (23} and (251 is 
subjected to ARIMA modeling techniques. The result of this process is 
an ARIMA(l,O,O) model of the PPI. (Again the statistical package DYNREG 
is able to handle the slight trend in the data thereby, negating the 
need to difference.) This model form defines the PPI data series as a 
random walk with a positive drift of about 3.5 percent per year. The 
fact that the PPI series turned out to be a random walk is encouraging 
because deflating price data series with this PPI series doesn't 
introduce new serial correlation problems. The general model form is: 
(26) PPit = a + {3 PPit- 1 + Ut, 
with Ut = Et. 
Where PPit-:1. is the PPI in the (t-i )th time frame, and ut is the error 
process CMA£0)). 
This model is estimated over the 1966 through 2nd quarter 1986 time 
frame. PPI predictions are obtained from this model by recursively 
forecasting 18 quarters. These forecasted values are the ones that will 
be used to convert to nominal price predictions the real price 
predictions made by the structural models examined. The exact model 
form obtained from the estimation is: 
( 27) 
with 
PPit = .012949 + .. 99243 PPit- 1 + Ut, 
(1.80) (103.51) 
ut = ~\ .i!. 
60 
Table 7 presents the predictions generated by this model. 
Table 7. PPI Predictions with a Random Walk Model 
Time Period Actual PPI Prediction 
1982 I 97.21 95.80 
1982 II 100.27 98.47 
1982 III 97.21 101.29 
1982 IV 96.15 98.12 
1983 I 98.43 97.12 
1983 II 99.18 99.39 
1983 II I 101.77 100.22 
1983 IV 101.30 102.74 
1984 I 105.22 102.41 
1984 II 103.22 106.19 
1984 III 101.96 104.08 
1984 IV 101.81 102.78 
1985 I 100.00 102.52 
1985 II 97.84 100.62 
1985 III 94.62 98.34 
1985 IV 99.21 95.26 
1986 I 97.13 99.74 
1986 II 98.11 97.69 
Utilizing the ARIMA(3,0,3) Model 
The ARIMA(3,0,3) model's forecasts succeeded in obtaining a Fama 
(1970) semi-strong form rejection of market efficiency. However, as 
pointed out by Rausser and Carter (1983), this represents only the 
necessary conditions for general market efficiency rejection. To meet 
the sufficiency requirements for efficiency rejection, the cost of 
c~nstructing and utilizing the ARIMA(3,0,3) must not exceed the 
incremental risk adjusted benefits. This section will attempt to 
quantify some of the costs of building and utilizing this model. A 
discussion of returns to price speculating with this model will also be 
61 
presented; however, risk adjustment of the returns is left to the 
reader. 
Since wheat price data and ARIMA procedures are quite 
straightforward, an ARIMA(3,0,3) model is relatively inexpensive to 
build. Computer charges for the time spent estimating and reestimating 
this model are approximately $500 and the opportunity cost of the time 
spent building this model is estimated at $1000. The marginal cost of 
running the ARIMA(3,0,3) model once it is constructed is so close to 
zero that it is assumed to be zero. Therefore, the total cost. of 
building and running this model is estimated to be $1500. 
The next step is to determine how much money would have to be 
invested to utilize this model's price predictions. The minimum margin 
requirement to trade one wheat contract (5000 bushels) at a brokerage 
house is approximately $750. However, an adverse price movement of 
more than $.05 would result in margin calls, i.e. more money would be 
required than $750 to hold the average contract one quarter. Since one 
contract of wheat is worth approximately $15,000 and the maximum cash 
wheat price change for any given quarter in the first quarter 1982 to 
second quarter 1986 time period was $.88 ($4400), an initial margin 
amount of $5000 is deemed sufficient. 
The total cost of building and opening an account to operate this 
model sums to $6500. This model would have been utilized four and one­
half years if the test prediction period is ~atched. The "safe" 
alternative for this $6500 would be to invest it in a bank CD for the 
four year period. If this were done with a 10 percent interest rate, 
62 
the amount in the account at the end of four and one half years would be 
$9981.15. 
Assume, that now, rather than investing the money in a CD, the 
ARIMA(3,0,3) model is built to be used as a price speculation tool for 
the first quarter 1982 through second quarter 1986 test period. The 
trading rule that will be followed with one wheat contract per quarter 
(18 trades) will be: If, in quarter t, the ARIMA(3,0,3) model's price 
prediction for quarter t+1 is greater than the wheat futures market's 
t+l price prediction, then one (long) wheat futures contract with t+l 
maturity will be purchased , i.e. a "long" position will be established 
and held until contract maturity is reached. If, instead, the 
ARIMA(3,0,3) model's price prediction for quarter t+l is less than the 
wheat futures market's price prediction for t+l, then one (short) wheat 
futures contract with t+l maturity will be purchased, i.e. a "short• 
position will be established and held until contract maturity is 
reached. Table 8 presents the quarterly breakdown of earnings and 
losses that are obtained from following this rule. 
The gross return for trading this model is $17,250. If a 
commission of $70 per trade is charged, then the gross return is 
recalculated at $15,990.00. Assuming that no interest is paid on the 
brokerage house's accounts and that no money is removed from the account 
to be invested elsewhere, the total brokerage account dollar value at 
the end of the trading period would be $20,9900 (including the original 
amount invested). 
It is pertinent to note at this point that the previous assumptions 
are quite restrictive, but the intent was to assume the worst possible 
63 
investment scenario. In reality, most brokerage accounts pay interest, 
and, even if the brokerage account did not pay interest, any money above 
margin could be removed from the brokerage firm and placed in an 
interest bearing account. There also existed the possibility of 
increasing the number of contracts traded per quarter as the account 
value grew, thereby increasing returns. 
Table 8. Returns to Market Price Speculation Using the ARIMA(3,0,3) 
Model 
ARIMA(3,0,3) Futures 
Time Cash Model's Market's Position 
Period Price Prediction Prediction Established Return 
1982 I 3.59 3.57 4.20 5 3050.00 
1982 II 3.31 3.36 3.66 5 1750.00 
1982 II I 3.18 3.24 3.58 s 2000.00 
1982 IV 3.23 3.16 3.47 5 1200.00 
1983 I 3.36 3.24 3.37 5 50.00 
1983 II 3.53 3.36 3.45 s - 400.00 
1983 III 3.62 3.54 3.58 s - 200.00 
1983 IV 3.55 3.54 3.95 s 2000.00 
1984 I 3.57 3.52 3.55 5 - 100.00 
1984 II 3.51 3.41 3.44 5 - 350.00 
1984 III 3.47 3.43 3.62 s 750.00 
1984 IV 3.49 3.47 3.52 s 150.00 
1985 I 3.58 3.49 3.47 L 550.00 
1985 II 3.27 3.25 3.36 s 450.00 
1985 III 2.83 3.01 3.28 s 2250.00 
1985 IV 3.46 3.24 2.93 L 2650.00 
1986 I 3.40 3.30 3.43 5 150.00 
1986 II 2.52 2. 72 2.78 5 1300.00 
The resulting return to speculation is 19.5 percent per year even 
with the restrictive approach taken. Clearly there now needs to be a 
risk adjustment made to compensate for the fact that using an ARIMA 
64 
model to trade is quite risky. As to the exact extent of the risk 
adjustment, no comments will be made since risk adjustment is a subject. 
of personal judgment. If the risk adjustment is large enough that the 
real return after risk adjustment to speculation is Jess than 1~ 
percent, then sufficiency criterion for efficiency rejection will not be 
met; however, if a risk adjusted return of greater than 10 percent is 
obtained, then sufficiency criterion for market efficiency rejection 
wi 11 be met. No matter what the conclusion is on the sufficiency 
criterion requirements, it must be remembered that this conclusion may 
only be valid for the time period examined by this study. 
Another common approach taken in the literature to examine 
potential above average returns to a trading rule is to compare. the 
returns generated by using the trading rule to naive buy and hOld 
strategies. Following a naive buy and hold strategy for this 18 quarter 
time period results in a $10,850 loss. With a commission charge of $70 
per trade, this Joss become $12,110. Clearly, for this time period, the 
ARIMA(3,0,3) model's speculative approach is superior to a naive buy and 
hold strategy. However, the relatively poor performance of the buy and 
hold strategy can at least partially be explained by the fact that the 
wheat market's general overall trend was down in the period examined. 
If, instead, a naive sell and hold strategy is followed, the resulting 
return would be exactly opposite, i.e. a $10,850 profit is generated by 
a naive sell and hold strategy (with commission this is a $9590). 
No matter which naive strategy is followed, the speculative return 
from using the ARIMA(3,0,3) is still superior. This indicates that the 
ARIMA model is capturing some relevant information which allowed for 
65 
better than naive performance. These results fit into the framework of 
a Fama (1970) semi-strong market efficiency rejection; however, the 
problem of different risks for different strategies again prevents a 
judgment of whether sufficiency criteria for efficiency rejection are 
met. 
The general conclusion of this empirics chapter is that only one 
model, the ARIMAC3,0,3), fully met the criteria for a Fama (1970) 
rejection of market efficiency. As for whether this model meets 
sufficiency criteria for efficiency rejection, only conditional 
conclusions can be made because of the problems with ranking risk. 
66 
CHAPTER 4 
SUMMARY AND CONCLUSIONS 
This chapter is broken into three sections. The first section 
briefly summarizes the steps undertaken by this study. The second 
section discusses any conclusions made from the results obtained by 
this study. 
research. 
The third section presents some suggestions for further 
Summary 
Futures market efficiency is of concern to both market traders and 
non-market participants since it relates the performance of a market in 
allocating resources through time. A problem exists in testing for 
market efficiency because the precise criteria for defining exactly 
what characteristics are consistent with market efficiency are obtuse, 
i.e. 
only 
beyond 
the tests taken for market efficiency are often limited to testing 
one particular definition of efficiency and have little meaning 
the particular definition chosen. In this study, the Chicago 
Board of Trade's wheat futures market was examined to see if the 
hypothesis of market efficiency, as defined by Fama (1970), could be 
rejected. The Fama (1970) approach to efficiency was taken because of 
its popularity in the relevant literature and because of its concisely 
defined tests. 
67. 
The first step of this study was to determine if the quarterly cash 
wheat market followed a random walk model. The rejection of the 
hypothesis that the cash wheat market follows a random walk provided a 
Fama (1970) weak ~orm rejection of market efficiency and indicated the 
possibility of developing an ARIMA model other than the ARIMA(l,O,Ol 
model to forward predict price. 
The subsequent steps that were taken in this study all find their 
basis in the concept that, if a forward price predicting model is shown 
to forecast future price "better" than the relevant futures market, then 
this constitutes a Fama (1970) semi-strong market efficiency rejection. 
The models that were used in this study were either built through ARIMA 
modeling procedures or selected from publicly available literature. 
Box and Jenkin's (1976) ARIMA(p,d,q) modeling procedures were 
followed to create an ARIMA(3,0,3) model of the quarterly cash price 
wheat market. The ARIMA(3,0,3) model was used to one step ahead 
forecast wheat prices for the first quarter 1982 through second quarter 
1986 time frame. The price forecasts obtained were compared, on the 
basis of RMSE and bias, to price predictions made by the Chicago Board 
of Trade's wheat futures market. A Fama (1970) semi-strong rejection of 
market efficiency was obtained on the basis of these comparisons. 
Two other forward wheat price predicting models were chosen from 
the relevant literature in order to compare, on the basis of RMSE and 
bias, their forward price predictions to the Chicago Board of Trade's 
wheat futures markets forward price predictions. Although both models 
enjoy some popularity in the literature, neither was able to reject the 
hypothesis that the Chicago Board of Trade's wheat future's market is 
68 
efficient. This can be partially explained by the fact that the 
creators of these models were probably as concerned with explaining 
market structural relationships as they were with forward price 
prediction. 
Since Fama•s 1970 work on efficiency is dated, this study undertook 
a final step to see if any conclusions on a later definition of 
efficiency could be obtained, i.e. a Fama (1970) rejection of efficiency 
represented only the rejection of the necessary conditions for 
p 
efficiency rejection, and is not sufficient for a general rejection of 
market efficiency. To meet the sufficiency criteria for market 
efficiency rejection, costs and risk have to be accounted for. As a 
result, this study simulated price speculation with the ARIMAC3,0,3) 
model for the first quarter 1982 through second quarter 1986 time frame. 
A 19.5 percent after cost rate of return was obtained by the 
ARIMA(3,0,3) for this time period. There is, however, a certain amount 
of risk involved in using an ARIMA model to forecast price, and the 
level of risk in using an ARIMA model to forecast price cannot be 
assumed equal to the level of risk faced by users of the futures market. 
As a result, the returns generated by the ARIMA(3,0,3) model need to be 
adjusted for risk before they are compared to returns generated by 
"safe" investments such as cos. However, this study did not determine a 
satisfactory way to adjust for risk that would reflect individual risk 
preferences and the risk of using ARIMA models to forecast price. Not 
adjusting for risk made impossible any conclusions concerning whether or 
not the sufficient conditions for market efficiency rejection, as 
defined by Rausser and Carter (1983), were met. 
69 
Conclusions 
Since efficiency studies are based only on a particular definition 
ana/or test of efficiency, any general conclusions reached will be 
subject to limitations. This results in the tendency of rejecting the 
hypothesis of market efficiency when, in fact, the market may really be 
"efficient." As a result of the previously stated problems, 
implications of the wheat market efficiency rejection that will be 
subsequently presented are limited, and should not be inferred to imply 
more tha·n the fact that a potent a 1 problem may exist. 
For the first quarter 1982 through second quarter 1986 time period 
this study was able to reject the hypothesis of. market efficiency. This 
implies that some objectionable resource allocations may have been 
present during this time frame. For example, farmers who based planting 
decisions on the Chicago Board of Trade's forecast of future wheat price 
could potentially have been misallocating too many resources to wheat 
production, i.e. the $.12 positive bias found to exist in the wheat 
future's 
resources 
Chicago 
market throughout this time period may have caused too 
to be allocated to wheat production. The large RMSE of 
Board of Trade's wheat futures market (relative to 
many 
the 
the 
ARIMA(3,0,3J model's RMSEJ also indicates that the through time resource 
allocations initiated because of the forward price predictions of the 
futures market were consistently more inaccurate than resource 
allocations based upon the price predictions of the ARIMA(3,0,3) model 
would have been. 
70 
As to whether the resource misallocations that are potentially 
indicated by this study are just a function of the type of tests used or 
the time period ex~mined, little can be said. Information is costly and 
price speculation is risky, so perhaps no objectionable inaccuracies 
exist. The wheat futures markets have, for approximately 100 years, 
provided a forward forecast of price at low cost to the user, and cannot 
be assigned the label of "inefficient" without a great deal more proof 
than was presented here. This study claims only to have rejected the 
Fama (1970) definition of efficiency, thereby indicating the slight 
probability that objectionable inaccuracies do exist in the wheat 
futures market. 
Further Research 
Even though the very definition of the word efficiency is obtuse to 
economists, the analysis of futures markets on the basis of variance 
and bias offers important contributions as to how well resources are 
being allocated. 
forecast length. 
This study looked at but one futures market and one 
There exist many markets and many forecast lengths 
that could benefit from some examination as long as the results from the 
examinations are taken at face value and not used to infer too much. 
Some specific research that this author would like to see 
undertaken includes: (1) extension of the length of the forward price 
predictions of the wheat market to see at which forecast length the 
lagged price terms quit revealing market stickiness, i.e. finding what 
forecast length could be appropriately represented with a random walk 
model; (2) tests to see if any significance can be placed on price chart 
71 
pattern formations that are advocated by technical market analysts as 
price prediction tools; (3) development of a test for efficiency that 
takes into account the risks of using trading rules to speculate and 
thereby allows an accurate measurement of the risk adjusted return 
received by speculators; and (4) measurements based on actual trading 
records of whether speculators, as a group or individually, can forecast 
price. If speculators are shown to be unable to forecast price and 
hence earn below average returns, then research needs to be done to 
explain why "rational" individuals chose to participate in a 
consistently losing endeavor. 
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73 
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American Economic 
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77 
Table 9. Original Data Set 
Moving 
Cash Total Ending Average Cash 
Date PPI Wheat Use Stocks Use Corn 
1966 I 39.04 1.63 419.00 917.30 000.00 1.19 
1966 II 39.12 1. 79 382.40 535.20 000.00 1.20 
1966 II I 39.55 1.86 411.40 1435.60 000.00 1. 32 
1966 IV 39.20 1.80 387.60 1049.10 400.10 1.28 
1967 I 39.12 1.80 349.20 700.10 382.56 1. 27 
1967 II 39.36 1.58 275.40 425.00 355.90 1 .26' 
1967 III 39.32- 1. 51 388.20 1559.30 350.10 1.15 
1967 IV 39.55 1.46 347.40 1212.10 340.05 1.02 
1968 I 40.06 1.50 372.90 839.50 345.98 1.06 
1968 II 40.26 1. 30 300.40 539.40 352.22 1.07 
1968 II I 40.38 1.20 430.90 1684.90 362.90 1. 01 
1968 IV 40.65 1. 33 339.40 1345.70 360.90 1.02 
1969 I 41.36 1. 32 233.60 1112.40 326.07 1.09 
1969 II 41 .91 1.28 294.20 818.60 324.53 1.16 
1969 I II 42.07 1. 31 403.90 1875.20 317.78 1.17 
1969 IV 42.62 1.48 341.70 1534.50 318.35 1.09 
1970 I 43.17 1. 53 337.60 1197.70 344.35 1.13 
1970 II 43.32 1. 41 314.10 884.70 349.33 1.18 
1970 II I 43.60 1.64 870.80 1731.60 466.05 1. 30 
1970 IV 43.60 1.68 378.70 1410.00 475.30 1.33 
1971 I 44.38 1.63 349.90 1060.40 478.38 1. 43 
1971 I I 44.89 1. 52 237.90 822.80 459.32 1. 41 
1971 III 44.97 1. 58 568.10 1873.80 383.65 1.22 
1971 IV 45.33 1.65 326.30 1547.60 370.55 1.02 
1972 I 46.11 1.67 337.30 1210.70 367.40 1.09 
1972 II 46.66 1". 61 227.50 983.40 364.80 1.14 
1"972 III 47.21 2.02 659.10 1870.90 387.55 1.16 
1972 IV 48.27 2.60 472.20 1399.00 424.02 1.27 
1973 I 50.98 2.37 472.10 927.30 457.72 1. 37 
1973 II 53.42 2.82 330.40 597 .1 0 483.45 1.67 
1973 III 54.87 5.11 856.80 1451.60 532.87 2.29 
1973 IV 55.70 5.84 523.60 928.30 545.72 2.25 
1974 I 59.47 5.59 380.50 548.10 522.82 2.68 
1974 II 61.15 3.91 209.60 340.10 492.62 2.48 
1974 III 65.67 4.41 562.00 1562.10 418.92 3.19 
.1974 IV 67.36 4.60 455.20 1107.50 401.82 3.35 
1975 I 66.93 3.62 445.80 662.10 418.15 2.86 
1975 II 68.22 3.03 227.30 435.00 422.57 2.67 
1975 I II 69.80 4.06 676.70 1885.80 451.25 2.81 
1975 IV 70.19 3.32 500.00 1386.60 462.45 2.44 
1976 I 70.54 3.66 449.60 937.40 463.40 2.47 
1976 II 71.92 3.47 272.40 665.60 474.67 2.60 
78 
Table 9. Continued 
Moving 
Cash Total Ending Average Cash 
Date PPI Wheat Use Stocks Use Corn 
1976 III 72.55 2.89 624.90 2190.40 461.72 2.69 
1976 IV 73.49 2.66 407.20 1783.60 438.52 2.20 
1977 I 74.98 2.63 393.00 1390.90 424.37 2.34 
1977 II 75.22 2.29 278.80 1113.20 425.97 2.23 
1977 III 72.27 2.20 755.10 2404.50 458.52 1. 70 
1977 IV 74.43 2.65 407.90 1997.00 458.70 1.84 
1978 I 78.55 2.82 467.50 1529.90 477.32 2.06 
1978 II 82.64 3.18 352.40 1177.80 495.72 2.27 
1978 II I 82.29 3.42 820.00 2133.90 511.95 2.05 
1978 IV 84.88 3.68 503.60 1630.80 535.87 2.03 
1979 I 89.95 3.79 401.90 1229.40 519.47 2.17 
1979 II 89.95 4.36 305.60 924.10 507.77 2.37 
1979 I II 91.04 4.28 788.10 2270.80 499.80 2.56 
1979 IV 92.14 4.26 555.10 1716.20 512.67 2.35 
1980 I 92.26 4.18 491.60 1225.10 535.10 2.41 
1980 II 92.03 3.96 323.50 902.00 539.57 2.42 
1980 II I 100.67 4.38 810.20 2473.50 545.10 2.89 
1980 IV 100.75 4.54 569.90 1903.80 548.80 3.09 
1981 I 99.57 4.15 575.80 1329.10 569.85 3.22 
1981 II 99.88 3.60 340.40 989.10 574.07 3.22 
1981 II I 98.31 3.87 1074.70 2727.50 640.20 2.85 
1981 IV 94.66 3.86 556.20 2172.10 636.77 2.39 
1982 I 97.21 3.59 621.30 1551.20 648.15 2.48 
.1982 II 100.27 3.31 392.70 1159.40 661.22 2.57 
1982 II I 97.21 3.18 956.10 2969.50 631.57 2.45 
1982 IV 96.15 3.23 466.30 2506.10 609.10 2.12 
1983 I 98.43 3.36 646.90 1862.00 615.50 2.54 
1983 II 99.18 3.53 347.60 1515.10 604.22 3.01 
1983 II I 101 .71 3.62 981.20 2955.20 610.50 3.27 
1983 IV 101.30 3.55 629.70 2326.40 651.35 3.16 
1984 I 105.22 3.57 569.40 1758.10 631.97 3.16 
1984 II 103.22 3.51 360.30 1398.60 635.15 3.34 
1984 III 101.96 3.47 1258.80 2467.00 704.55 3.11 
1984 IV 101.81 3.49 601.90 2139.80 697.60 2.59 
1985 I 100.00 3.58 475.10 1667.10 674.02 2.64 
1985 II 97.84 3.27 243.70 1425.20 644.87 2.67 
1985 III 94.62 2.83 885.00 2971.10 551.42 2.44 
1985 IV 99.21 3.46 450.30 2536.40 510.62 2.20 
1986 I 97.13 3.40 397.90 2130.10 494.23 2.31 
1986 II 98.11 2.52 227.90 1905.00 490.52 2.34