Using Orthogonal GARCH to Forecast Covarince Matrix of Stock Returns
The motivation of this paper is to study the estimation problems in large dimension systems in quantitative finance. The paper firstly presents principal component analysis to obtain the most important information in the data. Then, the orthogonal GARCH model introduced by Alexander and Chibumba (1997) and Alexander (2000) is provided to forecast five energy stocks’ monthly volatilities and correlations. I show that as long as the stocks are already highly correlated with one another, the orthogonal GARCH approach will reduce computational complexity, control the amount of ‘noise’, and produce volatility and correlations for all the assets. All the computation procedures were accomplished in Microsoft Excel. Forecasting of volatility and correlation of stock returns is significant in the analysis of option pricing, portfolio optimization and value-at-risk models.