Forecasting large covariance matrices: comparing autometrics and LASSOVAR

Abstract

This study aims to compare the performance of two well known automatic model selection algorithms, Autometrics (Hendry and Krolzig, 1999; Doornik, 2009), LASSOVAR and adaptive LASSOVAR (Callot et al., 2017) for modelling and forecasting monthly covariance matrices. To do so, we compose a database with daily information for 30 Brazilian stocks, which yields 465 unique entries, from July/2009 to December/2017. We apply three forecasting error measures, the model confidence set (Hansen et al., 2011) and Giacomini and White (2006) conditional test in the comparison. We also calculate the economic value for each of the forecasting strategy through a portfolio selec- tion exercise. The results show that the individual models are not able to beat the benchmark, the random walk, but a weighted combination of them is able to increase precision up to 13%. The portfolio selection exercises find that there are economic gains for using automatic model selection techniques to model and forecast the covariance matrices. Specifically, under short-selling constraint, Autometrics VAR(1) with dummy saturation delivers the highest Sharpe-ratio and economic value. When the investor is able to short-sell, ei- ther Autometrics VAR(1) with dummy saturation or adaptive Lasso VAR(1) is preferable. This final choice depend on the risk aversion of the investor. If he is less risk-averse, he prefers the former, while the latter becomes his choice if his risk-aversion sensitivity increases.