Multivariate stochastic volatility models based on generalized Fisher transformation

Abstract

Modeling multivariate stochastic volatility (MSV) can pose significant challenges, particularly when both variances and covariances are time-varying. In this study, we tackle these complexities by introducing novel MSV models based on the generalized Fisher transformation (GFT) proposed by Archakov and Hansen (2021). Our model exhibits remarkable flexibility, ensuring the positive-definiteness of the variance–covariance matrix, and disentangling the driving forces of volatilities and correlations. To conduct Bayesian analysis of the models, we employ a Particle Gibbs Ancestor Sampling (PGAS) method, facilitating efficient Bayesian model comparisons. Furthermore, we extend our MSV model to cover leverage effects and incorporate realized measures. Our simulation studies demonstrate that the proposed method performs well for our GFT-based MSV model. Furthermore, empirical studies based on equity returns show that the MSV models outperform alternative specifications in both in-sample and out-of-sample performances.