On partial-sum processes of ARMAX residuals
Steffen Grønneberg, Benjamin Holcblat
The Annals of Statistics · 2019 · Volume 47 · Issue 6
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.
Keywords
60F17, 62J20, 62M10, 91B84, ARMAX residuals, Autocorrelated errors, Change-point problems, CUSUM test, heteroscedastic errors, infinite-variance errors, kernel density estimation of ARMAX errors, linear and nonlinear regression, misspecified ARMAX, nonlinear ARMAX, seasonal dummy, weak GARCH
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