A model-free power transformation to homoscedasticity

Time series modelling explains most of the variation in color television sales over time. However, severe heteroscedasticity makes forecasting sensitive to forecast origin. A distribution context independent method, of regressing the logarithms of the absolute error in fitting a first-order autoregression against the logarithms of the original series is given for exact determination of the exponent of a variance stabilization power transformation. The distribution-free (free of the speciflc forecasting model and the attendant assumption of normality) estimate is compared with the model specific Box-Cox transformation, and found to have the practical advantages of being direct, automatic, faster and therefore cheaper to implement, and more robust. Some important applications include sales and inventory forecasting for distribution requirements planning in global logistics, forecasting for scheduling in-just-in time operations, and information feed forward for continuous process control.