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.
Publié le : 2008-10-15
Classification:
Empirical process,
long-memory time series,
residuals,
unit root,
weak convergence,
62G30,
62M10
@article{1223908099,
author = {Chan, Ngai Hang and Ling, Shiqing},
title = {Residual empirical processes for long and short memory time series},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 2453-2470},
language = {en},
url = {http://dml.mathdoc.fr/item/1223908099}
}
Chan, Ngai Hang; Ling, Shiqing. Residual empirical processes for long and short memory time series. Ann. Statist., Tome 36 (2008) no. 1, pp. 2453-2470. http://gdmltest.u-ga.fr/item/1223908099/