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We implement gradient-based variational inference routines for Wishart andinverse Wishart processes, which we apply as Bayesian models for the dynamic,heteroskedastic covariance matrix of a multivariate time series. The Wishartand inverse Wishart processes are constructed from i.i.d. Gaussian processes,existing variational inference algorithms for which form the basis of ourapproach. These methods are easy to implement as a black-box and scalefavorably with the length of the time series, however, they fail in the case ofthe Wishart process, an issue we resolve with a simple modification into anadditive white noise parameterization of the model. This modification is alsokey to implementing a factored variant of the construction, allowing inferenceto additionally scale to high-dimensional covariance matrices. Throughexperimentation, we demonstrate that some (but not all) model variantsoutperform multivariate GARCH when forecasting the covariances of returns onfinancial instruments.

Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processes