Diagnostic Tests for Innovations of ARMA Models Using Empirical Processes of Residuals

51 Pages Posted: 16 Apr 2010 Last revised: 2 Jul 2011

See all articles by Kilani Ghoudi

Kilani Ghoudi

United Arab Emirates University

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Date Written: June 30, 2010

Abstract

In view of applications to diagnostic tests of ARMA models, the asymptotic behavior of multivariate empirical and copula processes based on residuals of ARMA models is investigated.

Multivariate empirical processes based on squared residuals and other functions of the residuals are also investigated. It is shown how these processes can be used to develop distribution free tests of change-point analysis and serial independence. It is also demonstrated that these empirical processes provide an easy mechanism for developing goodness-of-fit tests for the distribution of the innovations, and that the well-known Lilliefors test can be applied to the residuals of ARMA models without any change.

Keywords: Diagnostic Tests, ARMA Models, Residuals, Squared Residuals, Empirical Processes, Coplas

JEL Classification: C52, C15, C12, C14

Suggested Citation

Ghoudi, Kilani and Remillard, Bruno, Diagnostic Tests for Innovations of ARMA Models Using Empirical Processes of Residuals (June 30, 2010). Available at SSRN: https://ssrn.com/abstract=1590823 or http://dx.doi.org/10.2139/ssrn.1590823

Kilani Ghoudi

United Arab Emirates University ( email )

Al-Ain, POB 17555
United Arab Emirates

Bruno Remillard (Contact Author)

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

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