Locally adaptive factor processes for multivariate time series

TL;DR

This paper introduces a locally adaptive factor process for multivariate time series that captures time-varying smoothness in mean and covariance, improving inference and prediction accuracy.

Contribution

It proposes a novel continuous-time model with nested Gaussian processes for locally adaptive smoothness, enabling efficient Bayesian inference.

Findings

Effective in simulations for capturing local smoothness variations.

Improves predictive interval calibration in financial data.

Reduces computational bottlenecks with differential equation representation.

Abstract

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to mis-calibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a locally adaptive factor process for characterizing multivariate mean-covariance changes in continuous time, allowing locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions evolving in time through nested Gaussian processes and linearly related to the observed data with a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application.