rfBLT: Random Feature Bayesian Lasso Takens Model for time series forecasting

TL;DR

The paper introduces rfBLT, a non-parametric Bayesian model for time series forecasting that captures complex dynamics, quantifies uncertainty, and outperforms traditional and machine learning models on real-world data.

Contribution

It proposes a novel rfBLT model combining Takens' theorem, random features, and Bayesian Lasso for improved time series prediction with uncertainty quantification.

Findings

rfBLT performs comparably to traditional models on simulated data.

rfBLT significantly outperforms other models on real-world data.

The method is implemented in an accessible R package.

Abstract

Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In contrast, machine learning models excel at learning complex patterns and handling high-dimensional data; however, they are unable to quantify the uncertainty associated with their predictions, as statistical models do. To overcome these drawbacks, we propose Random Feature Bayesian Lasso Takens (rfBLT) for forecasting time series data. This non-parametric model captures the underlying system via the Takens' theorem and measures the degree of uncertainty with credible intervals. This is achieved by projecting delay embeddings into a higher-dimensional space via random features and applying regularization within the Bayesian framework to identify relevant terms. Our results demonstrate that the rfBLT method is comparable to traditional statistical models on simulated data, while significantly outperforming both conventional and machine learning models when evaluated on real-world data. The proposed algorithm is implemented in an R package, rfBLT.