Multivariate stochastic volatility using state space models

TL;DR

This paper introduces a Bayesian state space model for multivariate stochastic volatility, allowing efficient online estimation of time-varying correlations in high-dimensional financial data.

Contribution

It generalizes the inverted Wishart distribution and extends convolution methods to model volatility evolution, enabling fast and flexible sequential updates.

Findings

Efficient estimation of time-varying correlations in high-dimensional data

Fast and computationally cheap volatility updating algorithm

Successful application to foreign exchange rates data

Abstract

A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the convolution between the Wishart and the multivariate singular beta distribution. A multiplicative model based on the generalized inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility and a flexible sequential volatility updating is employed. The proposed algorithm for the volatility is fast and computationally cheap and it can be used for on-line forecasting. The methods are illustrated with an example consisting of foreign exchange rates data of 8 currencies. The empirical results suggest that time-varying correlations can be estimated efficiently, even in situations of high dimensional data.