On the use of multi-step cost functions for generating forecasts

Accurate forecasts are of principal importance for operations. Exponential smoothing is widely used due to its simplicity, relatively good forecast accuracy, ease of implementation and automation. The literature has continuously improved upon many of its initial limitations, yet novel applications of exponential smoothing have brought new forecasting challenges that have revealed additional pitfalls in its use. In this work, we examine potential reasons for these issues and argue that special attention should be drawn to the cost function used to estimate model parameters. Conventional cost functions assume that the postulated model is an accurate reflection of underlying demand, which is not the case for the majority of real applications. We propose the use of alternative cost functions based on multi-step ahead predictions and trace forecasts. We show that these are univariate shrinkage estimators. We describe the nature of shrinkage and show that it differs from established shrinkage approaches, such as ridge and LASSO regression, offering new modelling capabilities. Using retailing sales, we construct forecasts and empirically demonstrate this shrinkage, validate our theoretical understanding, and provide evidence of both economic and forecast accuracy gains. We discuss implications for practice and limitations of the shrinkage caused by the multi-step cost functions