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Bilinear markovian representation and bilinear models

Author

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  • Pham, Dinh Tuan

Abstract

An extension of the linear Markovian repsentation called the bilinear Markovian representation is introduced, and is shown to provide representations of all-diagonal bilinear time series models. Some properties of the bilinear Markovian representation are also given.

Suggested Citation

  • Pham, Dinh Tuan, 1985. "Bilinear markovian representation and bilinear models," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 295-306, September.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:2:p:295-306
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    Citations

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    Cited by:

    1. Iqbal Owadally, 2014. "Tail risk in pension funds: an analysis using ARCH models and bilinear processes," Review of Quantitative Finance and Accounting, Springer, vol. 43(2), pages 301-331, August.
    2. Sumalee, A. & Zhong, R.X. & Pan, T.L. & Szeto, W.Y., 2011. "Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 507-533, March.
    3. Francesco Giordano & Marcella Niglio & Cosimo Damiano Vitale, 2023. "Linear approximation of the Threshold AutoRegressive model: an application to order estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 27-56, March.
    4. Guegan, Dominique & Wandji, Joseph Ngatchou, 1996. "Power of the Lagrange multiplier test for certain subdiagonal bilinear models," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 201-212, September.
    5. 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.
    6. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.
    7. D. A. Peel & A. E. H. Speight, 1998. "The variance of economic activity over the business cycle: some further evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 5(11), pages 669-673.
    8. Liu, Weidong & Lin, Zhengyan, 2009. "Strong approximation for a class of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 249-280, January.
    9. Bibi, Abdelouahab & Lescheb, Ines, 2012. "On general periodic time-varying bilinear processes," Economics Letters, Elsevier, vol. 114(3), pages 353-357.
    10. Bibi, Abdelouahab & Oyet, Alwell J., 2002. "A note on the properties of some time varying bilinear models," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 399-411, July.

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