Theses and Dissertations at Montana State University (MSU)
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Item A Monte Carlo study of several regression estimators in the context of second-order autocorrelation(Montana State University - Bozeman, College of Agriculture, 1988) Zidack, Walter Ernest; Chairperson, Graduate Committee: Myles Watts.The purpose of this study is to compare the small sample properties of several estimators in the context of second-order autocorrelation by using Monte-Carlo methods. Each estimator is applied to data sets generated under several experimental design assumptions. The design assumptions consist of four structures on the independent variable, iterated over two types of error structures, with each error structure being iterated over twenty-five combinations of the autoregressive parameters evenly distributed Within the second-order autoregressive stability triangle. The four independent variable structures included: (1) white noise; (2) dampened trend; (3) growth trend; and (4) dampened cyclical trend. The error structures are generated first under the assumption that the process is stationary, and second under the assumption that the process is initially nonstationary. Each permutation of the experimental design consists of a sample size of T=25, with each permutation being replicated 2500 times. Several statistics relevant to the selection of an appropriate estimator based on efficiency, computational complexities, and inference validity of each estimator are offered. From an overall perspective of choosing an estimator that uniformly demonstrates robustness across the various independent variable types, error structure assumptions, and autoregressive parameter values, a general ranking of the estimators is apparent. The ranking of these estimators is: (1) full maximum likelihood; (2) initially nonstationary; (3) Prais-Winsten estimators; and (4) Cochrane-Orcutt estimators. Ordinary least squares, however, is the superior estimator when the distance of the point defined by the value of the autoregressive parameters is close to the center of the second-order autoregressive stability triangle. The performance of the initially nonstationary estimator is not substantially below that of the full maximum likelihood estimator when viewed from the perspective of overall performance across the various subexperimental designs. This result coupled with the ease in implementing the initially nonstationary estimator for any order autoregressive process suggests strong potential tor this estimator to efficiently estimate linear regression models with autoregressive errors.Item The small sample properties of a nonstandard estimator in the context of first order autocorrelation(Montana State University - Bozeman, College of Agriculture, 1987) Siebrasse, Paul Benjamin; Chairperson, Graduate Committee: Jeffrey T. LaFrance.The purpose of this study is to compare the small sample properties of a nonstandard estimator for first order autocorrelated errors in a time series equation with those of the more widely used estimators by using Monte Carlo experiments. The estimation method of interest arises either from the assumption that the presample residuals are not generated from an autoregressive process or from fixing the estimates of the presample values of the residuals at their unconditional expectations. This method has several nice properties. First, the estimator that is obtained is asymptotically equivalent to the standard methods. Second, the initial observations in the sample are retained, which overcomes problems that can arise in small samples when the independent variables are trended. Third, the data transformation that is used to estimate the unknown parameters of the model can be generalized to any order autoregressive process without any substantial increase in complexity. The results indicate that this nonstandard estimator performs very well relative to the other estimators considered for most experimental designs. This implies that the costs of using this more convenient estimation technique in terms of accuracy of parameter estimates is low relative to the other techniques considered.