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On some probabilistic properties of double periodic AR models

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  • Aknouche, Abdelhakim
  • Guerbyenne, Hafida

Abstract

This paper deals with some probabilistic properties of the class of periodic autoregressions (PAR) with periodic ARCH innovations (PAR-PARCH). Under some suitable assumptions an equivalent random coefficient periodic autoregression formulation of the periodic ARCH equation is proposed, leading to a double periodic autoregression (DPAR) formulation for the model. Periodic stationarity and existence of higher-order moment properties of such a DPAR model are studied and from which we deduce those of the PAR-PARCH process.

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  • Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "On some probabilistic properties of double periodic AR models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 407-413, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:407-413
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    1. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    2. Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, July.
    3. Bera, Anil K & Higgins, Matthew L & Lee, Sangkyu, 1992. "Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 133-142, April.
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    5. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, September.
    6. repec:bla:jecsur:v:16:y:2002:i:3:p:245-69 is not listed on IDEAS
    7. W. K. Li & Shiqing Ling & Michael McAleer, 2002. "Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
    8. Taylor, James W., 2006. "Density forecasting for the efficient balancing of the generation and consumption of electricity," International Journal of Forecasting, Elsevier, vol. 22(4), pages 707-724.
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    Cited by:

    1. Aknouche, Abdelhakim & Rabehi, Nadia, 2024. "Inspecting a seasonal ARIMA model with a random period," MPRA Paper 120758, University Library of Munich, Germany.

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