Published online by Cambridge University Press: 02 November 2009
In this chapter, we evaluate the impact of parameter-estimation uncertainty on forecast-error uncertainty, from the perspective of multi-step (or dynamic) estimation (DE). Advocates of DE argue that when a model is mis-specified, minimization of 1-step errors may not deliver reliable forecasts at longer lead times, so that estimation by minimizing the in-sample counterpart of the desired stepahead horizon may be advantageous. We delineate conditions which favour DE for multi-step forecasting. An analytical example shows how DE may accommodate incorrectly-specified models as the forecast lead alters, improving forecast performance for some mis-specifications. However, in well-specified models, reducing finite-sample biases does not justify DE. In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favour DE, though other solutions exist to that scenario. A second Monte Carlo study obtains the estimator biases and explains these using asymptotic approximations.
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