A new taxonomy for vector exponential smoothing and its application to seasonal time series

In short-term demand forecasting, it is often difficult to estimate seasonality accurately, owing to short data histories. However, companies usually have multiple products with similar seasonal demand patterns. A possible solution in this case is to use the components of several time series from a homogeneous family, thus estimating seasonal coefficients based on cross-sectional information. Motivated by this practical problem, we propose a new taxonomy of Parameters, Initial States and Components (PIC), which exploits homogeneous features of time series. We then apply this framework to vector exponential smoothing. We develop a model selection mechanism based on information criteria to select the appropriate PIC restrictions. We then conduct a simulation experiment and empirical analysis on retail data in order to assess the performance of point forecasts and prediction intervals of the models within this framework.