Should fixed coefficients be re‐estimated every period for extrapolation?

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Abstract
This paper demonstrates that forecast accuracy is not necessarily improved when fixed‐coefficient models are sequentially re‐estimated and used for prediction, after updating the database with the latest observation(s). It is argued that although sequential estimation may minimize the variances of predictors based on some classes of estimators, sequential estimation does not necessarily yield accurate predictions (i.e. predictions that are close to actual realizations). Minimizing the mean squared prediction error about the actual realization is a necessary condition for maximizing the probability that one predictor is more accurate than others. This minimization need not require, and may even exclude, the most recent data. It has been shown by an example that a prediction based on a nonsequential estimate of a stochastically varying coefficient model is superior to predictions based on several sequential estimates of the fixed‐coefficient models, including a random walk model.

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