Order selection for same-realization predictions in autoregressive processes

By Ching-Kang Ing, Ching-zong Wei. 2005

112 citations recorded by the source corpus.

Assume that observations are generated from an infinite-order autoregressive [AR(∞)] process. Shibata [Ann. Statist. 8 (1980) 147-164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose of predicting the future of an independent replicate, Akaike's information criterion (AIC) and its variants are asymptotically efficient. Although Shibata's concept of asymptotic efficiency has been widely accepted in the literature, it is not a natural property for time series analysis. This is because when new observations of a time series become available, they are not independent of the previous data. To overcome this difficulty, in this paper we focus on order selection for forecasting the future of an observed time series, referred to as same-realization prediction. We present the first theoretical verification that AIC and its variants are still asymptotically elficient (in the sense defined in Section 4) for same-realization predictions. To obtain this result, a technical condition, easily met in common practice, is introduced to simplify the complicated dependent structures among the selected orders, estimated parameters and future observations. In addition, a simulation study is conducted to illustrate the practical implications of AIC. This study shows that AIC also yields a satisfactory saute-realization prediction in finite samples. On the other hand, a limitation of AIC in same-realization settings is pointed out. It is interesting to note that this limitation of AIC does not exist for corresponding independent cases.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/456859d92802b850e7c29c77838918d61e658a36

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Citations in the corpus

PREDICTION‐FOCUSED MODEL SELECTION FOR AUTOREGRESSIVE MODELS (2007, background): “First, the single-series setting is discussed, for which the AIC has recently been proved to be an asymptotically efficient criterion (Ing & Wei, 2005).”
ACCUMULATED PREDICTION ERRORS, INFORMATION CRITERIA AND OPTIMAL FORECASTING FOR AUTOREGRESSIVE TIME SERIES (2007, unknown): “, West (1996), McCracken (2000), and Inoue and Kilian (2006).”
On same-realization prediction in an infinite-order autoregressive process (2003, background): “For independent-realization predictions, Shibata [17] showed that the MSPE of the least-squares predictor with order selected by AIC [1] will ultimately achieve the best compromise between ðk=NÞs2 and jja aðkÞjj2R: Motivated by Shibata’s result and the asymptotic equivalence just mentioned, we show ”
Model Selection (2018, methodology): “Recently, Ing and Wei (2005) have obtained parallel results for the case where one and the same realization of the process is used for the estimation, selection, and prediction step.”
Model Selection Techniques: An Overview (2018, background): “An alternative definition is based on the same-realization expectation that calculates the loss of the future of an observed time series [10].”
Averaging estimators for autoregressions with a near unit root (2010, background): “E (Wc(1)W (1)) = exp (c) 1 c : (28) Proof: Using (8) and the fact that dW (s) is an orthogonal process,”