Granger Causality Inference for High-Dimensional Nonlinear Time Series with a Deep Particle Filter

Music City Center 

Identifying Granger causality in high-dimensional time series is crucial for understanding their complex dependence structures and improving forecasting accuracy, particularly in fields such as finance and neuroscience. In this work, we propose a novel deep state-space model in which state transitions are jointly modeled using a deep neural network, while the measurement equation remains linear to facilitate downstream analysis. To efficiently handle long-term high-dimensional time series, we develop a scalable Bayesian deep particle filtering algorithm that tracks latent states and uncovers the temporal dependencies between time series. We establish the convergence properties of the proposed algorithm, ensuring its theoretical soundness. Our method offers a principled approach to discovering causal relationships in challenging high-dimensional time series applications. We demonstrate its effectiveness through both simulated data and real-world applications, including the one-minute log returns of Nasdaq stocks.

High-dimensional time series

Granger causality

Nonlinear state space models

Deep particle filtering

Bayesian deep neural networks 

Section on Statistical Computing