Open Access
June 2013 Moment bounds and mean squared prediction errors of long-memory time series
Ngai Hang Chan, Shih-Feng Huang, Ching-Kang Ing
Ann. Statist. 41(3): 1268-1298 (June 2013). DOI: 10.1214/13-AOS1110


A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction errors (MSPE) of the CSS predictor. These asymptotic expressions not only explicitly demonstrate how the multi-step MSPE of the CSS predictor manifests with the model complexity and the dependent structure, but also offer means to compare the performance of the CSS predictor with the least squares (LS) predictor for integrated autoregressive models. It turns out that the CSS predictor can gain substantial advantage over the LS predictor when the integration order is high. Numerical findings are also conducted to illustrate the theoretical results.


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Ngai Hang Chan. Shih-Feng Huang. Ching-Kang Ing. "Moment bounds and mean squared prediction errors of long-memory time series." Ann. Statist. 41 (3) 1268 - 1298, June 2013.


Published: June 2013
First available in Project Euclid: 13 June 2013

zbMATH: 1292.62099
MathSciNet: MR3113811
Digital Object Identifier: 10.1214/13-AOS1110

Primary: 62J02
Secondary: 60F25 , 62F12 , 62M10

Keywords: ARFIMA model , integrated AR model , Long-memory time series , mean squared prediction error , moment bound , multi-step prediction

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 3 • June 2013
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