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Econometrics Paper
Distribution Free Goodness-of-Fit Tests for Linear Processes
Miguel A. Delgado, Javier Hidalgo and Carlos Velasco
January 2005
Paper No' EM/2005/482:
Full Paper (pdf)

JEL Classification: C14; C22

Tags: nonparametric model checking; spectral distribution; linear processes; martingale decomposition; local alternatives; omnibus; smooth and directional tests; long-range alternatives

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’s Tp-process with estimated parameters, which converges in distribution to the standard Brownian Motion under the null hypothesis. We discuss tests of different nature such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.