Tuning forecasting algorithms for black swans

Forecasting algorithms based on exponential smoothing have smoothing factors, and it is often recommended that these be tuned to minimise an error measure on observed data. We show that forecasting algorithms such as simple exponential smoothing and Croston's method cannot always be optimally tuned to time series using any of several error measures. We propose a data augmentation approach: adding hypothetical non-stationary time series (which we call “black swans” as they represent unseen pathological cases) to the training data, and minimising a weighted error. The choice of black swans is a form of judgemental forecasting that requires experts to explicitly state their assumptions on unseen data.