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Periodic stationarity of random coefficient periodic autoregressions

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  • Aknouche, Abdelhakim
  • Guerbyenne, Hafida

Abstract

This paper studies periodic stationarity of a random coefficient periodic autoregression (RCPAR) which generalizes the standard random coefficient autoregressive (RCAR) model to the case where the deterministic parameters and the disturbance variances are periodically time-varying. Sufficient conditions for the existence of a (strictly and second-order) periodically stationary solution to the RCPAR equation are proposed. As an application, we study periodic stationarity of a class of periodic bilinear models and a periodic autoregression with periodic ARCH errors.

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  • Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 990-996, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:990-996
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    References listed on IDEAS

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    1. Bibi, Abdelouahab & Ringo Ho, Moon-ho, 2004. "Properties of some bilinear models with periodic regime switching," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 221-231, September.
    2. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    3. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 1999. "The sample ACF of a simple bilinear process," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 1-14, September.
    4. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    5. Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
    6. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    7. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
    8. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    9. 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. Bibi, Abdelouahab & Lescheb, Ines, 2012. "On general periodic time-varying bilinear processes," Economics Letters, Elsevier, vol. 114(3), pages 353-357.
    2. Bibi, Abdelouahab & Ghezal, Ahmed, 2017. "Asymptotic properties of QMLE for periodic asymmetric strong and semi-strong GARCH models," MPRA Paper 81126, University Library of Munich, Germany.

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