Random Feature Bayesian Lasso Takens Model for Time Series Forecasting

Abstract

Time series prediction is challenging due to limited understanding of underlying dynamics; furthermore, the full state is rarely observable. Conventional models, such as ARIMA and Holt's linear trend, experience difficulty in identifying nonlinear patterns. In contrast, machine learning models excel at learning complex patterns but are unable to quantify uncertainty as statistical models do. To overcome these drawbacks, we propose Random Feature Bayesian Lasso Takens (rfBLT). This framework leverages Takens' Theorem to reconstruct dynamical systems from a single observed variable across the required number of historical time points. The delay embeddings are projected into a higher-dimensional space using random features. Regularization within the Bayesian framework is applied to identify relevant terms and quantify uncertainty via credible intervals. Our results demonstrate that rfBLT is comparable to traditional models on simulated data, while significantly outperforming conventional and machine learning models on real-world data. The algorithm is implemented in an R package, rfBLT.