Portmanteau Tests for Arma Models with Infinite Variance
نویسنده
چکیده
Autoregressive and moving-average (ARMA) models with stable Paretian errors is one of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem of diagnostic checking fitted models has not been addressed. In this paper, we develop portmanteau tests for checking randomness of a time series with infinite variance and for ARMA diagnostic checking when the innovations have infinite variance. It is assumed that least-squares or an asymptotically equivalent estimation method, such as Gaussian maximum likelihood, is used. And it is assumed that the distribution of the innovations is IID stable Paretian. It is seen via simulation that the proposed portmanteau tests do not converge well to the corresponding limiting distributions for practical series length so a Monte-Carlo test is suggested. Simulation experiments show that the proposed Monte-Carlo test procedure works effectively. Two illustrative applications to actual data are provided to demonstrate that an incorrect conclusion may result if the usual portmanteau test based on the finite variance assumption is used.
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تاریخ انتشار 2006