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December 2019 On partial-sum processes of ARMAX residuals
Steffen Grønneberg, Benjamin Holcblat
Ann. Statist. 47(6): 3216-3243 (December 2019). DOI: 10.1214/18-AOS1776

Abstract

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.

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Steffen Grønneberg. Benjamin Holcblat. "On partial-sum processes of ARMAX residuals." Ann. Statist. 47 (6) 3216 - 3243, December 2019. https://doi.org/10.1214/18-AOS1776

Information

Received: 1 July 2017; Revised: 1 August 2018; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/18-AOS1776

Subjects:
Primary: 60F17, 62J20, 62M10
Secondary: 91B84

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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