Residual empirical processes for long and short memory time series

Abstract

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov-Smirnov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992-1024] does not hold when the stochastic regression model includes an unknown intercept or when the characteristic polynomial of the unstable autoregressive model has a unit root. To this end, two new statistics are proposed to test for the distribution of the long-memory noises of stochastic regression models and unstable autoregressive models. (With Correction.)

Published in at http://dx.doi.org/10.1214/07-AOS543 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Fitting an error distribution in some heteroscedastic time series models

Cited by in corpus (1)

• Marked empirical processes for non-stationary time series