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

Naoya Katayama

Hi-Stat Discussion Paper Series from Institute of Economic Research, Hitotsubashi University

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.

Keywords: Mean-squared prediction errosrs; Long memory; Seasonality; Nonlinear least squares estimators; Convergence of moments (search for similar items in EconPapers)
JEL-codes: C22 C53 (search for similar items in EconPapers)
Date: 2004-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:hst:hstdps:d03-10

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