A Simple and Effective Random Forest Modelling for Nonlinear Time Series Data

TL;DR

This paper introduces RF-RW, a novel random forest method tailored for nonlinear time series data that preserves temporal dependence and improves prediction accuracy over existing models.

Contribution

It presents RF-RW, a theoretically justified random forest variant that maintains serial dependence and offers strong consistency guarantees for time series forecasting.

Findings

RF-RW outperforms existing RF-based methods in simulations.

RF-RW achieves lower prediction errors than SVM and LSTM.

RF-RW provides accurate COVID-19 case forecasts.

Abstract

In this paper, we propose Random Forests by Random Weights (RF-RW), a theoretically grounded and practically effective alternative RF modelling for nonlinear time series data, where existing RF-based approaches struggle to adequately capture temporal dependence. RF-RW reconciles the strengths of classic RF with the temporal dependence inherent in time series forecasting. Specifically, it avoids the bootstrap resampling procedure, therefore preserves the serial dependence structure, whilst incorporates independent random weights to reduce correlations among trees. We establish non-asymptotic concentration bounds and asymptotic uniform consistency guarantees, for both fixed- and high-dimensional feature spaces, which extend beyond existing theoretical analyses of RF. Extensive simulation studies demonstrate that RF-RW outperforms existing RF-based approaches and other benchmarks such as SVM and LSTM. It also achieves the lowest error among competitors in our real-data example of predicting UK COVID-19 daily cases.