Ching-Kang Ing

Multistep Prediction In Autoregressive Processes

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h > 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction models coefficients directly by linear least squares. Under rather mild conditions, asymptotic expressions for the mean-squared prediction errors (MSPEs) of these two predictors are obtained in stationary cases. In addition, we also extend these results to models with deterministic time trends. Based on these expressions, performances of the plug-in and direct predictors are compared. Finally, two examples are given to illustrate that some stationary case results on these MSPEs can not be generalized to the nonstationary case.The author is deeply grateful to the co-editor Pentti Saikkonen and two referees for their helpful suggestions and comments on a previous version of this paper.

Order selection for same-realization predictions in autoregressive processes

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, Akaikes information criterion (AIC) and its variants are asymptotically efficient. Although Shibatas 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.

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

The predictive capability of a modification of Rissanens accumulated prediction error (APE) criterion, APE

On same-realization prediction in an infinite-order autoregressive process

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Selecting optimal multistep predictors for autoregressive processes of unknown order

,is investigated in infinite-order autoregressive (AR(

Time series and related topics : in memory of Ching-Zong Wei

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Uniform moment bounds of Fisher’s information with applications to time series

)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE

A Note on Mean‐squared Prediction Errors of the Least Squares Predictors in Random Walk Models

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Development of Service Quality Scale for Surgical Hospitalization

is obtained by summing these squared errors from stage

Model selection for integrated autoregressive processes of infinite order

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