On the Heteroskedastic-Autoregressive Specification of the Linear Regression Model

In this paper we examine, from a theoretical viewpoint, the generalized normal linear regression model with disturbances that are simultaneously heteroskedastic and autoregressive. In particular, the error specification of the model is a mixture of Amemiya’s linear heteroscedasticity structure with a stationary first-order autoregressive process. Given that the heteroskedastic variances are functions of the first-order autocorrelation coefficient, the estimators used in applied research cannot properly distinguish the estimations of the heteroskedastic and autoregressive parameters of the model. To avoid this problem, we introduce a multi-step estimation procedure, which has mainly theoretical interest, and is not suggested as an alternative to the well-known heteroskedasticity and autocorrelation consistent estimation used in applied econometric research. This estimation procedure facilitates the derivation of two distinct, theoretically important, generalized linear models, one with heteroskedastic and another with first-order autoregressive error terms. These two distinct models can be used for the theoretical examination of the finite-sample distributional properties of the estimators of the heteroskedastic and autoregressive parameters.