Bruce E. Hansen
"Interval Forecasts and Parameter Uncertainty"
Journal of Econometrics, (2006), 135, 377-398.
Forecast intervals generalize point forecasts to represent and incorporate
uncertainty. Forecast intervals calculated from dynamic models typically
sidestep the issue of parameter estimation. This paper shows how to
construct asymptotic forecast intervals which incorporate the uncertainty
due to parameter estimation. Our proposed solution is a simple proportional
adjustment to the interval endpoints, the adjustment factor depending on the
asymptotic variance of the interval estimates. Our analysis is in the
context of a forecasting equation with an error independent of the forecasting variables
but with unknown distribution. The
methods are illustrated with a simulation experiment and an application to
the U.S. monthly unemployment rate.
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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.