Modeling Multivariate Positive-Valued Financial Time Series using Sparse Logarithmic Vector Multiplicative Error Models with Multivariate Gamma Errors

Music City Center 

The logarithmic multiplicative error model (log-vMEM) has been useful in modeling and forecasting multivariate positive-valued financial time series. However, as the number of components in the vector increases, the number of parameters in the log-vMEM also increases, making their estimation computationally intensive. Our proposed approach describes regularized estimation via hierarchical lag structures for log-vMEM models with multivariate Gamma errors. The hierarchical lag structure based regularization is compared with using a non-convex penalty such as the Smoothly Clipped Absolute Deviation (SCAD) penalty, or the Minimax Convex Penalty (MCP). We apply the proposed method to model the joint dynamics of robust intraday realized volatility measures for Microsoft.