Moment bounds and mean squared prediction errors of long-memory time series

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/105851

Title:	Moment bounds and mean squared prediction errors of long-memory time series
Authors:	黃士峰;Chan, Ngai Hang;Huang, Shih-Feng;Ing, Ching-Kang
Contributors:	理學院統計研究所
Keywords:	60F25;62F12;62J02;62M10;ARFIMA model;Asymptotic methods;Autoregressive moving average;Forecasting models;Input output;integrated AR model;Least squares;long-memory time series;Mathematical models;Mathematical moments;mean squared prediction error;Measurement errors;Modeling;moment bound;multi-step prediction;Parameter estimation;Parametric models;Statistics and Probability;Statistics, Probability and Uncertainty;Studies;Time series;Time series forecasting;Time series models
Date:	2013-06-01
Issue Date:	2026-04-23 12:57:54 (UTC+8)
Publisher:	Institute of Mathematical Statistics;Hayward: Institute of Mathematical Statistics
Abstract:	摘要： 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 multistep 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. 出版者： Hayward: Institute of Mathematical Statistics 出版日期： 2013-06-01 出處： The Annals of Statistics, 2013-06, Vol.41 (3), p.1268-1298 資源來源： JSTOR Arts and Sciences I 版權： Copyright © 2013 Institute of Mathematical Statistics 版權： Copyright Institute of Mathematical Statistics Jun 2013 版權： Copyright 2013 Institute of Mathematical Statistics 識別號： ISSN: 0090-5364 識別號： EISSN: 2168-8966 識別號： DOI: 10.1214/13-aos1110
Appears in Collections:	[Graduate Institute of Statistics] journal & Dissertation

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