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On general periodic time-varying bilinear processes

Author

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  • Bibi, Abdelouahab
  • Lescheb, Ines

Abstract

We study in this note the class of bilinear processes with periodic time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of strict and second order stationary solutions (in periodic sense) and for the existence of higher order moments. The given conditions can be applied to periodic ARMA or periodic GARCH models. The central limit theorem and the law of iterated logarithm (LIL) for higher order sample moments are showed.

Suggested Citation

  • Bibi, Abdelouahab & Lescheb, Ines, 2012. "On general periodic time-varying bilinear processes," Economics Letters, Elsevier, vol. 114(3), pages 353-357.
    • Handle: RePEc:eee:ecolet:v:114:y:2012:i:3:p:353-357
    DOI: 10.1016/j.econlet.2011.11.013
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    References listed on IDEAS

    as
    1. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    2. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    3. Pham, Dinh Tuan, 1985. "Bilinear markovian representation and bilinear models," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 295-306, September.
    4. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 990-996, April.
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    More about this item

    Keywords

    Periodic models; Bilinear processes; Periodic bilinear processes;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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