Regular variation of GARCH processes

B. Basrak, R.A. Davis, T. Mikosch

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    196 Citations (Scopus)
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    Abstract

    We show that the finite-dimensional distributions of a GARCH process are regularly varying, i.e., the tails of these distributions are Pareto-like and hence heavy-tailed. Regular variation of the joint distributions provides insight into the moment properties of the process as well as the dependence structure between neighboring observations when both are large. Regular variation also plays a vital role in establishing the large sample behavior of a variety of statistics from a GARCH process including the sample mean and the sample autocovariance and autocorrelation functions. In particular, if the 4th moment of the process does not exist, the rate of convergence of the sample autocorrelations becomes extremely slow, and if the second moment does not exist, the sample autocorrelations have non-degenerate limit distributions.
    Original languageEnglish
    Pages (from-to)95-115
    JournalStochastic Processes and their Applications
    Volume99
    Issue number1
    DOIs
    Publication statusPublished - 2002

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