Nonparametric extrapolative forecasting: An evaluation

This research evaluates the extension of nonparametric techniques into the extrapolative forecasting arena. Three nonparametric techniques are identified and developed for use with stationary time series, and three for use with linear trend series.;Techniques for stationary series are the running median, smoothed median, and Walsh average. Techniques for linear trend series are double running median, double smoothed median, and a variation of nonparametric robust regression. These techniques are compared to moving averages and Brown's exponential smoothing in a simulation and an empirical study.;Four error measures are used throughout this study: MAD, MSE, MAPE, and Theil's U. Each of these is consistent with a different loss function. A simulation study is performed to evaluate their joint behavior. Scatterplots and Spearman's correlations indicate that MAD, MSE, and MAPE tend to vary together under simulated changes in dispersion or probabilities of outliers. Theil's U does not relate well to MAD, MSE, or MAPE.;The simulation study disclosed that the parametric techniques were superior (as expected) on simple series with normal errors, and on simple series with Cauchy errors if there was a high level of first order autocorrelation. Nonparametric techniques were superior for series with Cauchy errors and a low level of first order autocorrelation.;The empirical study used the 111 series subset of the M-competition data. The data were deseasonalized, and the monotonic trend series were identified. The stationary techniques were evaluated on the series without monotonic trend, while the linear trend techniques were evaluated on the 92 monotonic trend series. Techniques were best fit using a grid search approach, with separate models possible for each of the error measures. All forecasts are made from the same time period. The techniques were evaluated over horizons from one to six. Results for the relative error measures indicate that the robust regression technique yielded better forecasts on average over horizons 1-6 than did Brown's double exponential smoothing.;The principal conclusion is that robust regression shows promise as an excellent forecasting technique that is relatively insensitive to underlying distributions and outliers.