Forecasting Volatility with Many Predictors

This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.