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

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Asymptotic Laws and Methods in Stochastics

Part of the book series: Fields Institute Communications ((FIC,volume 76))

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.

This paper is dedicated to Professor Miklós Csörgő on his 80th birthday.

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Acknowledgements

Funding in partial support of this work was provided by the National Research Foundation of the United Arab Emirates, the Natural Sciences and Engineering Research Council of Canada, the Fonds québécois de la recherche sur la nature et les technologies, and Desjardins Global Asset Management.

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Authors and Affiliations

  1. Department of Statistics, United Arab Emirates University, 17555, Al Ain, United Arab Emirates

    Kilani Ghoudi

  2. CRM, GERAD and Department of Decision Sciences, HEC Montréal, 3000 chemin de la Côte Sainte-Catherine, Montréal, QC, H3T 2A7, Canada

    Bruno Rémillard

Authors
  1. Kilani Ghoudi
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  2. Bruno Rémillard
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Corresponding author

Correspondence to Kilani Ghoudi .

Editor information

Editors and Affiliations

  1. School of Mathematics & Statistics, Herzberg Laboratories, Ottawa, Ontario, Canada

    Donald Dawson

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada

    Rafal Kulik

  3. School of Mathematics & Statistics, Carleton University, Ottawa, Ontario, Canada

    Mohamedou Ould Haye

  4. School of Mathematics & Statistics, Carleton University, Ottawa, Ontario, Canada

    Barbara Szyszkowicz

  5. School of Mathematics & Statistics, Carleton University, Ottawa, Ontario, Canada

    Yiqiang Zhao

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Ghoudi, K., Rémillard, B. (2015). Diagnostic Tests for Innovations of ARMA Models Using Empirical Processes of Residuals. In: Dawson, D., Kulik, R., Ould Haye, M., Szyszkowicz, B., Zhao, Y. (eds) Asymptotic Laws and Methods in Stochastics. Fields Institute Communications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3076-0_14

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