A Quantile Regression Approach to Generating Prediction Intervals
Exponential smoothing methods do not involve a formal procedure for identifying the underlying data generating process. The issue is then whether prediction intervals should be estimated by a theoretical approach, with the assumption that the method is optimal in some sense, or by an empirical procedure. In this paper we present an alternative hybrid approach which applies quantile regression to the empirical fit errors to produce forecast error quantile models. These models are functions of the lead time, as suggested by the theoretical variance expressions. In addition to avoiding the optimality assumption, the method is nonparametric, so there is no need for the common normality assumption. Application of the new approach to simple, Holt's, and damped Holt's exponential smoothing, using simulated and real data sets, gave encouraging results.
Volume (Year): 45 (1999)
Issue (Month): 2 (February)
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- Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
- Wilpen L. Gorr & Cheng Hsu, 1985. "An Adaptive Filtering Procedure for Estimating Regression Quantiles," Management Science, INFORMS, vol. 31(8), pages 1019-1029, August.
- Yar, Mohammed & Chatfield, Chris, 1990. "Prediction intervals for the Holt-Winters forecasting procedure," International Journal of Forecasting, Elsevier, vol. 6(1), pages 127-137.
- Rosas, A. Lorena & Guerrero, Victor M., 1994. "Restricted forecasts using exponential smoothing techniques," International Journal of Forecasting, Elsevier, vol. 10(4), pages 515-527, December.
- Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
- Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
- Chatfield, Chris & Yar, Mohammed, 1991. "Prediction intervals for multiplicative Holt-Winters," International Journal of Forecasting, Elsevier, vol. 7(1), pages 31-37, May.
- S. A. Roberts, 1982. "A General Class of Holt-Winters Type Forecasting Models," Management Science, INFORMS, vol. 28(7), pages 808-820, July.
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