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Constructing Prediction Intervals: A Re-Edition of the Williams-Goodman Method

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DOI: 10.4236/ojs.2019.92017    205 Downloads   437 Views


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.

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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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