Untransformed first observation problem in regression model with moving average process

Abstract

This paper shows the impact of underestimation of variance of an estima-tor when first observation is left untransformed to simplify the computational procedure. In fact, the bias of the variance is not diminishing even for large sample size for the model considered. By partitioning the covariance matrix into two parts, this paper explains why least square estimator with untrans-formed first observation shows such a consequence. To demonstrate this, an exact GLS estimator is developed by modifying an approximate estimator. Nonetheless, the computational simplicity remains same.