Modeling Realized Covariance Measures with Heterogeneous Liquidity: A Generalized Matrix-Variate Wishart State-Space Model

Abstract

We propose to generalize the Wishart state-space model for realized covariance matrices of asset returns in order to capture complex measurement error structures induced by heterogeneous liquidity across assets. Our model assumes that the latent covariance matrix of the assets is observed through their realized covariance matrix with a Riesz measurement density, which generalizes the Wishart to monotone missing data. The Riesz alleviates the Wishart-implied attenuation of measurement errors for less liquid assets and translates into a convenient likelihood factorization which facilitates inference using simple Bayesian MCMC procedures. The statespace approach allows for a flexible description of the covariance dynamics implied by the data and an empirical application shows that the model performs very well in- and out-of-sample.