Improve Orthogonal GARCH with Hidden Markov Model

Abstract: Orthogonal Generalized Autoregressive Conditional Heteroskedasticity model (OGARCH) is widely used in finance industry to produce volatility and correlation forecasts. We show that the classic OGARCH model, nevertheless, tends to be too slow in reflecting sudden changes in market condition due to excessive persistence of the integral univariate GARCH processes. To obtain more flexibility to accommodate abrupt market changes, e.g. financial crisis, we extend classic OGARCH model by incorporating a two-state Markov regime-switching GARCH process. This novel construction allows us to capture recurrent systemic regime shifts. Empirical results show that this generalization resolves the problem of excessive persistency effectively and greatly enhances OGARCH's ability to adapt to sudden market breaks while preserving OGARCH's most attractive features such as dimension reduction and multi-step ahead forecasting. By constructing a global minimum variance portfolio (GMVP), we are able to demonstrate significant outperformance of the extended model over the classic OGARCH model and the commonly used Exponentially Weighted Moving Average (EWMA) model. In addition, we show that the extended model is superior to OGARCH and EWMA in terms of predictive accuracy.