A Simple Method of Computing Prediction Intervals for Time Series Forecasts

Theoretical approaches to computing prediction intervals require strong assumptions that do not appear to hold in practice. This paper presents an empirical approach to prediction intervals that assumes very little. During model-fitting, variances of the errors are computed at different forecast leadtimes. Using these variances, the Chebyshev inequality is applied to determine prediction intervals. Empirical evidence is presented to show that this approach gives reasonable results. For example, using the 111 series in the M-competition, 95% prediction intervals actually contain 95.8% of post-sample observations.