Constructing Prediction Intervals: A Re-Edition of the Williams-Goodman Method ()
ABSTRACT
The aim of this paper is to develop and validate a procedure for
constructing prediction intervals. These forecasts are produced by Box-Jenkins
processes with external deterministic regressors and prediction intervals are
based on the procedure proposed by Williams-Goodman in 1971. Specifically, the
distributions of forecast error at various lead-times are determined using
post-sample forecast errors. Fitting a density function to each distribution
provides a good alternative to simply observing the errors directly because, if
the fitting is satisfactory, the quantiles of the distribution can be estimated
and then the interval bounds computed for different time origins. We examine a
wide variety of probability densities to search the one that best fit the empirical
distributions of forecast errors. The most suitable mathematical form results
to be Johnson’s system of density functions. The results obtained with several
time series suggest that a Box-Jenkins process combined with the
Williams-Goodman procedure based on Johnson’s distributions, provide accurate
prediction intervals.
Share and Cite:
Amerise, I. and Tarsitano, A. (2019) Constructing Prediction Intervals: A Re-Edition of the Williams-Goodman Method.
Open Journal of Statistics,
9, 230-244. doi:
10.4236/ojs.2019.92017.
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