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Diagnostic Checking Of Periodic Autoregression Models With Application

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  • A. I. McLeod

Abstract

. An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development:identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving‐average models.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:2:p:221-233
    DOI: 10.1111/j.1467-9892.1994.tb00186.x
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    Cited by:

    1. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
    2. Eduardo Rossi & Dean Fantazzini, 2015. "Long Memory and Periodicity in Intraday Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 13(4), pages 922-961.
    3. 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.
    4. Ooms, M. & Franses, Ph.H.B.F., 1998. "A seasonal periodic long memory model for monthly river flows," Econometric Institute Research Papers EI 9842, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Haldrup, Niels & Hylleberg, Svend & Pons, Gabriel & Sanso, Andreu, 2007. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 21-32, January.
    6. 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).
    7. Franses, Philip Hans & Ooms, Marius, 1997. "A periodic long-memory model for quarterly UK inflation," International Journal of Forecasting, Elsevier, vol. 13(1), pages 117-126, March.
    8. 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.
    9. T. Manouchehri & A. R. Nematollahi, 2019. "Periodic autoregressive models with closed skew-normal innovations," Computational Statistics, Springer, vol. 34(3), pages 1183-1213, September.
    10. Hugo Siqueira & Mariana Macedo & Yara de Souza Tadano & Thiago Antonini Alves & Sergio L. Stevan & Domingos S. Oliveira & Manoel H.N. Marinho & Paulo S.G. de Mattos Neto & João F. L. de Oliveira & Ive, 2020. "Selection of Temporal Lags for Predicting Riverflow Series from Hydroelectric Plants Using Variable Selection Methods," Energies, MDPI, vol. 13(16), pages 1-35, August.
    11. 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.
    12. 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.
    13. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    14. Luis E. Nieto-Barajas, 2022. "Dependence on a collection of Poisson random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 21-39, March.
    15. Hurd, H. & Makagon, A. & Miamee, A. G., 0. "On AR(1) models with periodic and almost periodic coefficients," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 167-185, July.
    16. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    17. repec:vuw:vuwscr:18989 is not listed on IDEAS
    18. Siem Jan Koopman & Marius Ooms, 2003. "Time Series Modelling of Daily Tax Revenues," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 439-469, November.
    19. Guthrie, Graeme & Videbeck, Steen, 2002. "High Frequency Electricity Spot Price Dynamics: An Intra-day Markets Approach," Working Paper Series 18989, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    20. 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.
    21. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    22. Guthrie, Graeme & Videbeck, Steen, 2002. "High Frequency Electricity Spot Price Dynamics: An Intra-day Markets Approach," Working Paper Series 3891, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    23. 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.

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