A Non-linear Forecast Combination Procedure for Binary Outcomes

We develop a non-linear forecast combination rule based on copulas that incorporate the dynamic interaction between individual predictors. This approach is optimal in the sense that the resulting combined forecast produces the highest discriminatory power as measured by the receiver operating characteristic (ROC) curve. Under additional assumptions, this rule is shown to be equivalent to the quintessential linear combination scheme. To illustrate its usefulness, we apply this methodology to optimally aggregate two currently used leading indicators—the ISM new order diffusion index and the yield curve spread—to predict economic recessions in the United States. We also examine the sources of forecasting gains using a counterfactual experimental set up.