Unrestricted Maximum Likelihood Estimation of Multivariate Realized Volatility Models

The popular conditional autoregressive Wishart (CAW) model for dynamics of realized covariance matrices provides a flexible parametrisation. However, the number of parameters grows quadratically with the number of assets, which causes enormous computational difficulties in higher dimensions. Therefore, its unrestricted maximum likelihood (ML) estimation up to now has been conducted only for small portfolios with around five assets. In this paper we elaborate on unrestricted ML estimation of the CAW model in higher dimensions for around 30 assets which is a sufficient number for portfolio diversification. We do so by providing various explicit analytical results for computing the gradient for log-likelihood optimization