Generalised Wishart Processes

TL;DR

The paper introduces the generalized Wishart process, a flexible stochastic model for dynamic covariance matrices that handles missing data, covariates, and scales efficiently, outperforming traditional models like GARCH.

Contribution

It presents a novel stochastic process with Wishart marginals for modeling time-varying covariance matrices, offering improved flexibility and scalability over existing models.

Findings

Outperforms multivariate GARCH in financial data modeling

Handles missing data and multiple covariates easily

Scales well with high-dimensional data

Abstract

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.