Locally adaptive factor processes for multivariate time series
This addresses the need for more accurate modeling of multivariate time series in fields like finance, but it appears incremental as it builds on existing factor process and Gaussian process methods.
The authors tackled the problem of modeling multivariate time series with time-varying smoothness in mean and covariance, which can lead to misleading inferences and mis-calibrated predictive intervals if not accounted for. They proposed a locally adaptive factor process that allows locally varying smoothness, and assessed its performance in simulations and a financial application.
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.