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Asymptotic prediction of mean squared error for long‐memory processes with estimated parameters
Author(s) -
Katayama Naoya
Publication year - 2008
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1078
Subject(s) - estimator , mathematics , asymptotic analysis , mean squared error , series (stratigraphy) , autoregressive model , parametric statistics , statistics , convergence (economics) , paleontology , biology , economics , economic growth
In this paper we deal with the prediction theory of long‐memory time series. The purpose is to derive a general theory of the convergence of moments of the nonlinear least squares estimator so as to evaluate the asymptotic prediction mean squared error (PMSE). The asymptotic PMSE of two predictors is evaluated. The first is defined by the estimator of the differencing parameter, while the second is defined by a fixed differencing parameter: in other words, a parametric predictor of the seasonal autoregressive integrated moving average model. The effects of misspecifying the differencing parameter is a long‐memory model are clarified by the asymptotic results relating to the PMSE. The finite sample behaviour of the predictor and the model selection in terms of PMSE of the two predictors are examined using simulation, and the source of any differences in behaviour made clear in terms of asymptotic theory. Copyright © 2008 John Wiley & Sons, Ltd.