Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processes
This work addresses the challenge of scalable Bayesian covariance modeling for time series, particularly in finance, but it is incremental as it builds on existing Gaussian process methods.
The authors tackled the problem of modeling dynamic covariance matrices in multivariate time series by implementing scalable variational inference for Wishart and inverse Wishart processes, with results showing that some variants outperform multivariate GARCH in forecasting financial returns covariances.
We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, existing variational inference algorithms for which form the basis of our approach. These methods are easy to implement as a black-box and scale favorably with the length of the time series, however, they fail in the case of the Wishart process, an issue we resolve with a simple modification into an additive white noise parameterization of the model. This modification is also key to implementing a factored variant of the construction, allowing inference to additionally scale to high-dimensional covariance matrices. Through experimentation, we demonstrate that some (but not all) model variants outperform multivariate GARCH when forecasting the covariances of returns on financial instruments.