Empirical processes for infinite variance autoregressive models

Chafik Bouhaddioui and Kilani Ghoudi

Journal of Multivariate Analysis, 2012, vol. 107, issue C, 319-335

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.

Keywords: Empirical process; Stable distributions; Infinite variance; Autoregressive models; Independence tests; Goodness-of-fit tests; Portmanteau statistics (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:107:y:2012:i:c:p:319-335

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DOI: 10.1016/j.jmva.2012.01.018

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