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A note on the properties of some time varying bilinear models

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  • Bibi, Abdelouahab
  • Oyet, Alwell J.

Abstract

In this note, a sufficient condition is given for the existence and uniqueness of a stable causal solution for bilinear time series with time-varying coefficients; also some conditions for invertibility and the optimal prediction procedure are given. The notions of controllability, observability and minimality are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:4:p:399-411
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    References listed on IDEAS

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    1. Marc Hallin, 1986. "Nonstationary q-dependent processes and time-varying moving average models: invertibility properties and the forecasting problem," ULB Institutional Repository 2013/2005, ULB -- Universite Libre de Bruxelles.
    2. Pham, Dinh Tuan, 1985. "Bilinear markovian representation and bilinear models," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 295-306, September.
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    1. Bibi, Abdelouahab, 2005. "A note on the stability and causality of general time-dependent bilinear models," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 131-138, June.
    2. 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.

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