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On multiplicative seasonal modelling for vector time series

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  • Ursu, Eugen
  • Duchesne, Pierre

Abstract

Many time series encountered in real applications display seasonal behavior. In this paper, we consider multiplicative seasonal vectorial autoregressive moving average (SVARMA) models to describe seasonal vector time series. We discuss conditional maximum likelihood estimation of the model parameters, allowing them to satisfy general linear constraints. Having fitted a model, residual autocovariances (or autocorrelations) have been found useful in checking time series models. Consequently, we obtain the asymptotic distributions of the residual autocovariance matrices. As applications of these results, Portmanteau test statistics are proposed and their asymptotic distributions are studied. The finite-sample properties of the test statistics are evaluated using Monte Carlo experiments.

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  • Ursu, Eugen & Duchesne, Pierre, 2009. "On multiplicative seasonal modelling for vector time series," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2045-2052, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:2045-2052
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    1. Gregory C. Reinsel & Sabyasachi Basu & Sook Fwe Yap, 1992. "Maximum Likelihood Estimators In The Multivariate Autoregressive Moving‐Average Model From A Generalized Least Squares Viewpoint," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 133-145, March.
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    3. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
    4. 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.
    5. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    6. D. S. Poskitt & M. O. Salau, 1995. "On The Relationship Between Generalized Least Squares And Gaussian Estimation Of Vector Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 617-645, November.
    7. Eugen Ursu & Pierre Duchesne, 2009. "Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 183-212, May.
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    1. Abdoulkarim Ilmi Amir & Yacouba Boubacar Maïnassara, 2020. "Multivariate portmanteau tests for weak multiplicative seasonal VARMA models," Statistical Papers, Springer, vol. 61(6), pages 2529-2560, December.

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