Empirical processes for infinite variance autoregressive models

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    1 Citation (Scopus)


    The paper proposes new procedures for diagnostic checking of fitted models under the assumption of infinite-variance errors which are in the domain of attraction of a stable law. These procedures are functional of residual-based empirical processes. First, the asymptotic distributions of the empirical processes based on residuals are derived. Then two important applications in time series diagnostics are discussed. A goodness-of-fit test is developed using a functional of the empirical process based on residuals. Tests of independence of innovations are also considered. The finite-sample behavior of these tests are studied by simulation and comparison with the classical Portmanteau tests for ARMA models with infinite-variance developed recently by Lin and McLeod (2008). [25] is provided.

    Original languageEnglish
    Pages (from-to)319-335
    Number of pages17
    JournalJournal of Multivariate Analysis
    Publication statusPublished - May 2012


    • Autoregressive models
    • Empirical process
    • Goodness-of-fit tests
    • Independence tests
    • Infinite variance
    • Portmanteau statistics
    • Stable distributions

    ASJC Scopus subject areas

    • Statistics and Probability
    • Numerical Analysis
    • Statistics, Probability and Uncertainty


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