Scandinavian Working Papers in Business Administration
Working Papers,
Örebro University, School of Business
No 2021:1: Singular conditional autoregressive Wishart model for realized covariance matrices
Gustav Alfelt (), Taras Bodnar (), Farrukh Javed () and Joanna Tyrcha ()
Additional contact information
Gustav Alfelt: Department of Mathematics, Stockholm University, Postal: Stockholm University, Department of Mathematics, SE-106 91 Stockholm, Sweden
Taras Bodnar: Department of Mathematics, Stockholm University, Postal: Stockholm University, Department of Mathematics, SE-106 91 Stockholm, Sweden
Farrukh Javed: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Joanna Tyrcha: Department of Mathematics, Stockholm University, Postal: Stockholm University, Department of Mathematics, SE-106 91 Stockholm, Sweden
Abstract: Realized covariance matrices are often constructed under the assumption that richness of intra-day return data is greater than the portfolio size, resulting in non-singular matrix measures. However, when for example the portfolio size is large, assets suffer from illiquidity issues, or market microstructure noise deters sampling on very high frequencies, this relation is not guaranteed. Under these common conditions, realized covariance matrices may obtain as singular by construction. Motivated by this situation, we introduce the Singular Conditional Autoregressive Wishart (SCAW) model to capture the temporal dynamics of time series of singular realized covariance matrices, extending the rich literature on econometric Wishart time series models to the singular case. This model is furthermore developed by covariance targeting adapted to matrices and a sectorwise BEKK-specification, allowing excellent scalability to large and extremely large portfolio sizes. Finally, the model is estimated to a 20 year long time series containing 50 stocks, and evaluated using out-ofsample forecast accuracy. It outperforms the benchmark Multivariate GARCH model with high statistical significance, and the sectorwise specification outperforms the baseline model, while using much fewer parameters.
Keywords: Covariance targeting; High-dimensional data; Realized covariance matrix; Stock co-volatility; Time series matrix-variate model
33 pages, October 2, 2020
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