Moving Average Correction in a Regression Model

Abstract

Some problems in the errors of regression model is an important issue, such as the autocorrelated error, moving average error. When these problems occur, the ordinary least squares (OLS) estimators can not be used because they are not efficient. This paper proposes a transformation matrix to correct the first-order moving average, MA(1), problem and to recover the one lost observation in a regression model. When the errors have the MA(1) problem, the sample mean squared error (MSE) is shown theoretically and empirically to be an overestimate of the MSE after transformation. The results of simulation study confirm that the errors after removing the MA(1) problem are independent and if the MA(1) problem is not corrected, the MSE overestimates the corrected one at the significance level 0.05.