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On stationarity and [beta]-mixing of periodic bilinear processes

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  • Bibi, Abdelouahab
  • Lessak, Radia

Abstract

This paper studies some probabilistic properties of periodic bilinear processes. In these nonlinear models, the parameters are allowed to switch between different regimes. Stationarity and geometric ergodicity conditions (in periodic sense) are given under general and tractable assumptions. We use these results to give necessary and sufficient conditions for stationarity of specific periodic GARCH processes which can be written as a periodic bilinear models. Moreover, it is shown that local stationarity i.e., stationarity within each regime, is not necessary to obtain global stationarity.

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  • Bibi, Abdelouahab & Lessak, Radia, 2009. "On stationarity and [beta]-mixing of periodic bilinear processes," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 79-87, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:79-87
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    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    2. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
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    1. Abdelouahab Bibi & Ahmed Ghezal, 2016. "On periodic time-varying bilinear processes: structure and asymptotic inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 395-420, August.

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