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Empirical processes for infinite variance autoregressive models

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  • Bouhaddioui, Chafik
  • Ghoudi, Kilani

Abstract

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.

Suggested Citation

  • Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:319-335
    DOI: 10.1016/j.jmva.2012.01.018
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    References listed on IDEAS

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