Combining Forecasts using Meta-Learning: A Comparative Study for Complex Seasonality

TL;DR

This paper tackles combining forecasts from heterogeneous models for time series with multiple seasonality by employing stacking via meta-learning. It introduces five meta-learners—$\text{LR}$, $\text{kNN}$, $\text{MLP}$, $\text{RF}$, and $\text{LSTM}$—with global and local learning variants, formalized as the ensemble forecast $\tilde{y}_t=f(\hat{\mathbf{y}}_t; \boldsymbol{\theta}_t)$. Through a large-scale study on 35 triple-seasonality time series using 16 base models, the authors demonstrate that meta-learners consistently outperform simple averaging, with $\text{RF}$ achieving the best $MAPE$ and $MdAPE$ and $\text{LSTM}$ achieving the best $MSE$. The findings highlight the value of nonlinear meta-learning for forecast combination in complex seasonal settings and point to future work on specialized sequential meta-models for time series tasks.

Abstract

In this paper, we investigate meta-learning for combining forecasts generated by models of different types. While typical approaches for combining forecasts involve simple averaging, machine learning techniques enable more sophisticated methods of combining through meta-learning, leading to improved forecasting accuracy. We use linear regression, $k$-nearest neighbors, multilayer perceptron, random forest, and long short-term memory as meta-learners. We define global and local meta-learning variants for time series with complex seasonality and compare meta-learners on multiple forecasting problems, demonstrating their superior performance compared to simple averaging.

Figures (5)

• Figure 1: Training points for LSTM in variants v1, v2 and v3.
• Figure 2: Importance scores of the forecasting models determined using MRMR and RReliefF methods.
• Figure 3: MAPE boxplots for the various ensemble variants.
• Figure 4: MAPE ranking.
• Figure 5: Results of the Diebold-Mariano tests.