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On efficient point prediction systems
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DOI：10.1111/1467-9868.00153.png)
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Abstract
En 中文
Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction system, 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.
Keywords:
efficiency
optimal predictors
point prediction systems
predictive inference
prequential inference
stochastic regression
time series
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