ON PARTIAL-SUM PROCESSES OF ARMAX RESIDUALS

• 成果类型: Article
• 署名作者: Gronneberg, Steffen; Holcblat, Benjamin
• 署名单位: BI Norwegian Business School; University of Luxembourg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1776
• 发表日期: 2019
• 页码: 3216-3243
• 关键词: cusum test; Empirical Process; structural-change; WEAK-CONVERGENCE; model-selection; least-squares; time-series; regression; variance; density

摘要

We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.