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On Stationarity Of The Solution Of A Doubly Stochastic Model

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  • Mohsen Pourahmadi

Abstract

. Consider the discrete parameter process {XI} satisfying the doubly stochastic model Xt=øtXt‐1+εt where {ø} and {εt} are also stochastic processes. Necessary and sufficient conditions on {ø} are given for {X1} to be a second order process. When {øt} is a strictly stationary process, some sufficient conditions in terms of {ø} are given which guarantee the wide sense stationarity of {Xt}. It turns out that for these problems the distribution and dependence structure of the process {log |ø|} play an important role.

Suggested Citation

  • Mohsen Pourahmadi, 1986. "On Stationarity Of The Solution Of A Doubly Stochastic Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(2), pages 123-131, March.
    • Handle: RePEc:bla:jtsera:v:7:y:1986:i:2:p:123-131
    DOI: 10.1111/j.1467-9892.1986.tb00490.x
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    Cited by:

    1. Wu, Jyh-Lin & Chen, Show-Lin, 2001. "Nominal exchange-rate prediction: evidence from a nonlinear approach," Journal of International Money and Finance, Elsevier, vol. 20(4), pages 521-532, August.
    2. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    3. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    4. Charemza, Wojciech W. & Deadman, Derek F., 1995. "Speculative bubbles with stochastic explosive roots: The failure of unit root testing," Journal of Empirical Finance, Elsevier, vol. 2(2), pages 153-163, June.

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