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Portmanteau tests for periodic ARMA models with dependent errors

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  • Y. Boubacar Maïnassara
  • A. Ilmi Amir

Abstract

In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving‐average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi‐squared random variables, which can be different from the usual chi‐squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self‐normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented.

Suggested Citation

  • Y. Boubacar Maïnassara & A. Ilmi Amir, 2024. "Portmanteau tests for periodic ARMA models with dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 164-188, March.
    • Handle: RePEc:bla:jtsera:v:45:y:2024:i:2:p:164-188
    DOI: 10.1111/jtsa.12692
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    1. A. I. McLeod, 1994. "Diagnostic Checking Of Periodic Autoregression Models With Application," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 221-233, March.
    2. A. I. McLeod, 1995. "Diagnostic Checking Of Periodic Autoregression Models With Application," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 647-648, November.
    3. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
    4. Xiaofeng Shao, 2010. "Corrigendum: A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 695-696, November.
    5. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
    6. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    7. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    8. Eugen Ursu & Pierre Duchesne, 2009. "On modelling and diagnostic checking of vector periodic autoregressive time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 70-96, January.
    9. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    12. repec:bla:jtsera:v:25:y:2004:3:p:359-372 is not listed on IDEAS
    13. Pierre Duchesne & Pierre Lafaye de Micheaux, 2013. "Distributions for residual autocovariances in parsimonious periodic vector autoregressive models with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 496-507, July.
    14. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.
    15. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    16. Robert Lund & I. V. Basawa, 2000. "Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 75-93, January.
    17. Ercan Balaban & Asli Bayar & Ozgur Berk Kan, 2001. "Stock returns, seasonality and asymmetric conditional volatility in world equity markets," Applied Economics Letters, Taylor & Francis Journals, vol. 8(4), pages 263-268.
    18. Xiaofeng Shao, 2012. "Parametric Inference in Stationary Time Series Models with Dependent Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 772-783, December.
    19. 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.
    20. Qin Shao & Robert Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.
    21. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
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