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

Ching-Kang Ing

Econometrics from EconWPA

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 $0 < \delta_{n} < 1$ may depend on $n$. Under certain regularity conditions, an asymptotic expression is derived for the mean-squared prediction error (MSPE) of an AR predictor with order determined by APE$_{\delta_{n}}$. This expression shows that the prediction performances of APE$_{\delta_{n}}$ can vary dramatically depending on the choice of $\delta_{n}$. Another interesting finding is that when $\delta_{n}$ approaches 1 at a certain rate, APE$_{\delta_{n}}$ can achieve asymptotic efficiency in most practical situations. An asymptotic equivalence between APE$_{\delta_{n}}$ and an information criterion with a suitable penalty term is also established from the MSPE point of view. It offers a new perspective for comparing the information- and prediction-based model selection criteria in AR($\infty$) models. Finally, we provide the first asymptotic efficiency result for the case when the underlying AR($\infty$) model is allowed to degenerate to a finite autoregression.

Keywords: Accumulated prediction errors; Asymptotic equivalence; Asymptotic efficiency; Information criterion; Order selection; Optimal forecasting (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2005-03-23
Note: Type of Document - pdf; pages: 50
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpem:0503020

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