Mixed pooling of seasonality for time series forecasting: An application to pallet transport data

TL;DR

This paper introduces a mixed hierarchical seasonality (MHS) model for time series forecasting that effectively captures multiple seasonal patterns and their interactions, outperforming traditional methods on real-world pallet transport data.

Contribution

The paper proposes a novel MHS model that learns the importance of each seasonal component and their interactions, improving forecasting accuracy over existing models.

Findings

MHS model outperforms Fourier, SARIMA, and complete pooling in prediction error.

The model effectively captures multiple seasonal patterns and their interactions.

Significant improvements in MAPE and ELPD on real-world data.

Abstract

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.