Mixed pooling of seasonality for time series forecasting: An application to pallet transport data
This work addresses forecasting challenges for business time series with dramatic seasonal effects, such as in logistics, though it appears incremental as it builds on existing hierarchical and mixture approaches.
The authors tackled the problem of forecasting time series with multiple seasonal patterns by proposing a mixed hierarchical seasonality (MHS) model, which achieved considerable improvements in out-of-sample prediction error (MAPE) and predictive density (ELPD) compared to existing models like complete pooling, Fourier decomposition, and SARIMA.
Multiple seasonal patterns play a key role in time series forecasting, especially for business time series where seasonal effects are often dramatic. Previous approaches including Fourier decomposition, exponential smoothing, and seasonal autoregressive integrated moving average (SARIMA) models do not reflect the distinct characteristics of each period in seasonal patterns. We propose a mixed hierarchical seasonality (MHS) model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is taken. This results in a model that automatically learns the relative importance of each seasonality and addresses the interactions between them. The model is implemented with Stan, a probabilistic language, and was compared with three existing models on a real-world dataset of pallet transport from a logistic network. Our new model achieved considerable improvements in terms of out of sample prediction error (MAPE) and predictive density (ELPD) compared to complete pooling, Fourier decomposition, and SARIMA model.