Mixed pooling of seasonality in time series pallet forecasting

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, such as the unique behavior of specific days of the week in business data. We propose a multi-dimensional hierarchical model. Intermediate parameters for each seasonal period are first estimated, and a mixture of intermediate parameters is then taken, resulting in a model that successfully reflects the interactions between multiple seasonal patterns. Although this process reduces the data available for each parameter, a robust estimation can be obtained through a hierarchical Bayesian model implemented in Stan. Through this model, it becomes possible to consider both the characteristics of each seasonal period and the interactions among characteristics from multiple seasonal periods. Our new model achieved considerable improvements in prediction accuracy compared to previous models, including Fourier decomposition, which Prophet uses to model seasonality patterns. A comparison was performed on a real-world dataset of pallet transport from a national-scale logistic network.