ACCUMULATED PREDICTION ERRORS, INFORMATION CRITERIA AND OPTIMAL FORECASTING FOR AUTOREGRESSIVE TIME SERIES

Abstract

The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE$_{\delta_{n}}$,is investigated in infinite-order autoregressive (AR($\infty$)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE$_{\delta_{n}}$ is obtained by summing these squared errors from stage $n\delta_{n}$, where $n$ is the sample size and $0Accumulated prediction errors, Asymptotic equivalence, Asymptotic efficiency, Information criterion, Order selection, Optimal forecasting