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Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations

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  • Yacouba Boubacar Maïnassara
  • Bruno Saussereau

Abstract

In this paper, we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving average models with uncorrelated but nonindependent innovations by using a self-normalization approach. We establish the asymptotic distribution of the proposed statistics. This asymptotic distribution is quite different from the usual chi-squared approximation used under the independent and identically distributed assumption on the noise, or the weighted sum of independent chi-squared random variables obtained under nonindependent innovations. A set of Monte Carlo experiments and an application to the daily returns of the CAC40 is presented. Supplementary materials for this article are available online.

Suggested Citation

  • Yacouba Boubacar Maïnassara & Bruno Saussereau, 2018. "Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1813-1827, October.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:524:p:1813-1827
    DOI: 10.1080/01621459.2017.1380030
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    Citations

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    Cited by:

    1. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    2. Cerovecki, Clément & Francq, Christian & Hörmann, Siegfried & Zakoïan, Jean-Michel, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 353-375.
    3. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for a class of multivariate asymmetric power GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 964-1002, November.
    4. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    5. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for the asymmetric power GARCH model when the power is unknown," Statistical Papers, Springer, vol. 63(3), pages 755-793, June.
    6. Hong, Yongmiao & Linton, Oliver & McCabe, Brendan & Sun, Jiajing & Wang, Shouyang, 2024. "Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach," Journal of Econometrics, Elsevier, vol. 238(2).
    7. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    8. Hajria, Raja Ben & Khardani, Salah & Raïssi, Hamdi, 2018. "A power comparison between autocorrelation based tests," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 1-6.
    9. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    10. Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.

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