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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.

Suggested Citation

  • Naoya Katayama, 2004. "Asymptotic Prediction Mean Squared Error for Strongly Dependent Processes with Estimated Parameters," Hi-Stat Discussion Paper Series d03-10, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:hstdps:d03-10
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    File URL: http://hi-stat.ier.hit-u.ac.jp/research/discussion/2003/pdf/D03-10.pdf
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    More about this item

    Keywords

    Mean-squared prediction errosrs; Long memory; Seasonality; Nonlinear least squares estimators; Convergence of moments;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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