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.
Citation
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
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