Forecasting volatility with macroeconomic and financial variables using Kernel Ridge Regressions

This paper uses the nonlinear method kernel ridge regression to forecast volatilities with 38 macroeconomic and financial variables of four different asset classes, i.e. stocks, bonds, commodities and foreign exchanges. Kernels which are used in this paper are the linear, quadratic and the Gaussian kernel. Tuning parameters of this method are estimated in two ways, i.e. with principal components and on the full dataset of variables. Furthermore, the Least Angle Regression method is used to preselect variables, which are then used by the kernel ridge regression. Next to examining this nonlinear method, 3-month, 6-month and 12-month ahead forecasts are made for kernel ridge regressions and numerous of other linear models. Main findings are that kernel ridge regression performs better than simple linear models, and multi-step ahead forecasts with macroeconomic and financial variables are not better than a simple autoregressive model.