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On efficient point prediction systems

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  • K. Skouras
  • A. P. Dawid

Abstract

Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t, issues a point prediction for the next observation at time t+1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of squared prediction errors. Independence is not a requirement. Under weak conditions, the class of efficient point prediction systems is non‐empty, and any two efficient point prediction systems will, in a certain strong sense, make asymptotically identical predictions for the infinite future. We discuss the efficiency of point prediction systems based on Bayesian predictive means, and on plugging in parameter estimates. The results are applied to probability forecasting and stochastic regression.

Suggested Citation

  • K. Skouras & A. P. Dawid, 1998. "On efficient point prediction systems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 765-780.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:4:p:765-780
    DOI: 10.1111/1467-9868.00153
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    Cited by:

    1. Mariola Pilatowska, 2010. "Choosing a Model and Strategy of Model Selection by Accumulated Prediction Error," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 10, pages 107-119.
    2. Mariola Pilatowska, 2011. "Information and Prediction Criteria in Selecting the Forecasting Model," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 11, pages 21-40.

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