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A Random Parameter Process For Modeling And Forecasting Time Series

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  • Deborah A. Guyton
  • Nien‐Fan Zhang
  • Robert V. Foutz

Abstract

. A generalized autoregressive (GAR) process {Z(t); t = 0, ±1, …} is defined to satisfy the recurrence relation Z(t) = Aθ (t)Z (t ‐l)+ u(t), where {Aθ(t); t = 0,±1, …} is itself a stochastic process depending on a vector parameter θ and where {u(t); t= 0, ±1, …} is white noise with Eu2 (t) =a2. This paper develops theory and methodology and implementing the class of GAR processes for time series modeling and forecasting. Conditions on the ‘parameter process’{Aθ (t); t= 0, ±1, …} are obtained for the existence of a GAR process; necessary and sufficient conditions on {Aθ (t); t= 0, ±1, …} for existence of a stationary GAR process are also obtained. Procedures are developed for computing maximum likelihood estimates of the parameters 0 and u2 and for computing the minimum mean squared error forecasts for GAR processes.

Suggested Citation

  • Deborah A. Guyton & Nien‐Fan Zhang & Robert V. Foutz, 1986. "A Random Parameter Process For Modeling And Forecasting Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(2), pages 105-115, March.
    • Handle: RePEc:bla:jtsera:v:7:y:1986:i:2:p:105-115
    DOI: 10.1111/j.1467-9892.1986.tb00488.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. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    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.

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