Asymptotic Prediction Mean Squared Error for Strongly Dependent Processes with Estimated Parameters

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Asymptotic Prediction Mean Squared Error for Strongly Dependent Processes with Estimated Parameters

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Naoya Katayama

Abstract

In this paper we deal with the prediction theory of long memory processes. After investigating the general theory relating to convergence of moments of the nonlinear least squares estimators, we evaluate the asymptotic prediction mean squared error of two predictors. One is defined by using the estimator of the differencing parameter and the other is defined by using a fixed, known differencing parameter, which is, in other words, one parametric predictor of the seasonally integrated autoregressive moving average (SARIMA) models. In this paper, results do not impose the normality assumption and deal not only with stationary time series but also with nonstationary ones. The finite sample behavior is examined by simulations using the computer program S-PLUS in terms of the asymptotic theory.

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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Hi-Stat Discussion Paper Series with number d03-10.

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Date of creation: Jan 2004
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Handle: RePEc:hst:hstdps:d03-10

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-01-25 (All new papers)
NEP-ECM-2004-01-25 (Econometrics)
NEP-ETS-2004-01-25 (Econometric Time Series)

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Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.

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