Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization

This paper introduces the Deep Functional Factor Model (DF 2 M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF 2 M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF 2 M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF 2 M. Empirical results from four real-world datasets demonstrate that DF 2 M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.