This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett Tp-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.
Publié le : 2005-12-14
Classification:
Nonparametric model checking,
spectral distribution,
linear processes,
martingale decomposition,
local alternatives,
omnibus,
smooth and directional tests,
long-range alternatives,
62G10,
62M10,
62F17,
62M15
@article{1140191667,
author = {Delgado, Miguel A. and Hidalgo, Javier and Velasco, Carlos},
title = {Distribution free goodness-of-fit tests for linear processes},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 2568-2609},
language = {en},
url = {http://dml.mathdoc.fr/item/1140191667}
}
Delgado, Miguel A.; Hidalgo, Javier; Velasco, Carlos. Distribution free goodness-of-fit tests for linear processes. Ann. Statist., Tome 33 (2005) no. 1, pp. 2568-2609. http://gdmltest.u-ga.fr/item/1140191667/