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On modelling and diagnostic checking of vector periodic autoregressive time series models

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  • Eugen Ursu
  • Pierre Duchesne

Abstract

. Vector periodic autoregressive time series models (PVAR) form an important class of time series for modelling data derived from climatology, hydrology, economics and electrical engineering, among others. In this article, we derive the asymptotic distributions of the least squares estimators of the model parameters in PVAR models, allowing the parameters in a given season to satisfy linear constraints. Residual autocorrelations from classical vector autoregressive and moving‐average models have been found useful for checking the adequacy of a particular model. In view of this, we obtain the asymptotic distribution of the residual autocovariance matrices in the class of PVAR models, and the asymptotic distribution of the residual autocorrelation matrices is given as a corollary. Portmanteau test statistics designed for diagnosing the adequacy of PVAR models are introduced and we study their asymptotic distributions. The proposed test statistics are illustrated in a small simulation study, and an application with bivariate quarterly West German data is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:1:p:70-96
    DOI: 10.1111/j.1467-9892.2008.00601.x
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    1. 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.
    2. Pierre Duchesne, 2005. "On the asymptotic distribution of residual autocovariances in VARX models with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 449-473, December.
    3. Parzen, Emanuel & Pagano, Marcello, 1979. "An approach to modeling seasonally stationary time series," Journal of Econometrics, Elsevier, vol. 9(1-2), pages 137-153, January.
    4. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030, Decembrie.
    5. 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.
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    1. 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.
    2. Christopher M. Schlick & Soenke Duckwitz & Sebastian Schneider, 2013. "Project dynamics and emergent complexity," Computational and Mathematical Organization Theory, Springer, vol. 19(4), pages 480-515, December.
    3. PEREAU Jean-Christophe & URSU Eugen, 2015. "Application of periodic autoregressive process to the modeling of the Garonne river flows," Cahiers du GREThA (2007-2019) 2015-14, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    4. Ursu, Eugen & Duchesne, Pierre, 2009. "On multiplicative seasonal modelling for vector time series," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2045-2052, October.
    5. Daniel Dzikowski & Carsten Jentsch, 2024. "Structural Periodic Vector Autoregressions," Papers 2401.14545, arXiv.org.
    6. T. Manouchehri & A. R. Nematollahi, 2019. "Periodic autoregressive models with closed skew-normal innovations," Computational Statistics, Springer, vol. 34(3), pages 1183-1213, September.
    7. Sarnaglia, A.J.Q. & Reisen, V.A. & Lévy-Leduc, C., 2010. "Robust estimation of periodic autoregressive processes in the presence of additive outliers," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2168-2183, October.
    8. Amaal Elsayed Mubarak & Ehab Mohamed Almetwally, 2024. "Modelling and Forecasting of Covid-19 Using Periodical ARIMA Models," Annals of Data Science, Springer, vol. 11(4), pages 1483-1502, August.
    9. Boubacar Maïnassara, Yacouba & Ursu, Eugen, 2025. "Diagnostic checking of periodic vector autoregressive time series models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 205(C).
    10. Yacouba Boubacar Maïnassara & Eugen Ursu, 2023. "Estimating weak periodic vector autoregressive time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 958-997, September.
    11. Francesco Battaglia & Domenico Cucina & Manuel Rizzo, 2020. "Detection and estimation of additive outliers in seasonal time series," Computational Statistics, Springer, vol. 35(3), pages 1393-1409, September.
    12. Stover, Oliver & Nath, Paromita & Karve, Pranav & Mahadevan, Sankaran & Baroud, Hiba, 2024. "Dependence structure learning and joint probabilistic forecasting of stochastic power grid variables," Applied Energy, Elsevier, vol. 357(C).

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