On the Use of Predictive Least Square Criterion in Economic Time Series

Abstract

In the linear time series literature, several criteria have been proposed to solve the order determination problem. One of the criteria proposed by Rissenan, is the predictive least square (PLS) principle. In two different contexts, Hemerly and Davis, Hannan, McDougall and Poskitt show the strong consistency of the PLS criterion in selecting the order for autoregression. Their results are based on the assumption that the conditional variance is homogeneous over time. Contrary to the linear time series modelling, there is lack of guidance in order determination for economic time series. Even the properties of some standard criteria such as AIC and BIC are unknown. We propose to use the PLS criterion to solve the order determination problem. The consistency property of the PLS criteria can still be obtained after the relaxation of the constant conditional variance assumption. Applications to some popular econometrics models such as ARCH and GARCH models will also be discussed.