Forecasting with Many Predictors : Allowing for Non-Linearity

While there is an extensive literature concerning forecasting with many predictors, there are but few attempts to allow for non-linearity in such a "data-rich environment". Using macroeconomic data, we show that substantial gains in forecast accuracy can be achieved by including both squares and first level interactions of the original variables in a predictive regression model. In case the number of original variables is reasonably large this requires specific econometric considerations though, as the number of parameters to be estimated may greatly exceed the number of available observations. We propose a two-stage "screen and clean" procedure that enables estimation and forecasting in this "ultrahigh-dimensional" setting. In the first stage, we perform univariate regressions to screen for truly interesting effects, controlling the False Discovery Rate. In the second step, we perform a standard bridge regression