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STATIONARITY OF THE SOLUTION OF Xt= AtXt‐1+εt AND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES

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  • MOHSEN POURAHMADI

Abstract

. We give general and concrete conditions in terms of the coefficient (stochastic) process {At} so that the (doubly) stochastic difference equation Xt= AtXt‐1+εt has a second‐order strictly stationary solution. It turns out that by choosing {At} and the “innovation” process {εt} properly, a host of stationary processes with non‐Gaussian marginals and long‐range dependence can be generated using this difference equation. Examples of such nowGaussian marginals include exponential, mixed exponential, gamma, geometric, etc. When {At} is a binary time series, the conditional least‐squares estimator of the parameters of this model is the same as those of the parameters of a Galton‐Watson branching process with immigration.

Suggested Citation

  • Mohsen Pourahmadi, 1988. "STATIONARITY OF THE SOLUTION OF Xt= AtXt‐1+εt AND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 225-239, May.
    • Handle: RePEc:bla:jtsera:v:9:y:1988:i:3:p:225-239
    DOI: 10.1111/j.1467-9892.1988.tb00467.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. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    3. George Kapetanios, 2002. "A Note on Covariance Stationarity Conditions for Dynamic Random Coefficient Models," Working Papers 475, Queen Mary University of London, School of Economics and Finance.
    4. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    5. 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.
    6. George Kapetanios, 2005. "Tests for Deterministic Parametric Structural Change in Regression Models," Working Papers 539, Queen Mary University of London, School of Economics and Finance.
    7. Kapetanios, George, 2008. "Bootstrap-based tests for deterministic time-varying coefficients in regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 534-545, December.
    8. Swaminathan, V. & Naik-Nimbalkar, U. V., 1997. "Minimum distance estimation for random coefficient autoregressive models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 313-322, June.

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