Singular conditional autoregressive Wishart model for realized covariance matrices

Realized covariance matrices are often constructed under the assumption that richness of intra-day return data is greater than portfolio size, resulting in nonsingular matrix measures. However, when for example size large, assets suffer from illiquidity issues, or market microstructure noise deters sampling on very high frequencies, this relation not guaranteed. Under these common conditions, realized may obtain as singular by construction. Motivated situation, we introduce Singular Conditional Autoregressive Wishart (SCAW) model to capture temporal dynamics time series matrices, extending rich literature econometric models case. This furthermore developed targeting adapted and a sector wise BEKK-specification, allowing excellent scalability large extremely sizes. Finally, estimated 20-year long containing 50 stocks 10-year 300 stocks, evaluated using out-of-sample forecast accuracy. It outperforms benchmark with statistical significance parsimonious specifications perform better baseline SCAW model, while considerably less parameters.