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Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models

Author

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  • Ord, J.K.
  • Koehler, A.
  • Snyder, R.D.

Abstract

A class of dynamic, nonlinear, statistical models is introduced for the analysis of univariate time series. A distinguishing feature of the models is their reliance on only one primary source of randomness: a sequence of independent and identically distributed normal disturbances. It is established that the models are conditionally Gaussian. This fact is used to define a conditional maximum likelihood method of estimation and prediction. A particular member of the class is shown to provide the statistical foundations for the multiplicative Holt-Winters method of forecasting. This knowledge is exploited to provide methods for computing prediction intervals to accompany the more usual point predictions obtained from the Holt-Winters method. The methods of estimation and prediction are evaluated by simulation. They are also illustrated with an application to Canadian retail sales.
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Suggested Citation

  • Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:1995-4
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