The small sample properties of a nonstandard estimator in the context of first order autocorrelation

Abstract

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.