Evaluating forecast performance with state dependence

We propose a novel forecast evaluation methodology to assess models' absolute and relative forecasting performance when it is a state-dependent function of economic variables. In our framework, the forecasting performance, measured by a forecast error loss function, is modeled via a hard or smooth threshold model with unknown threshold values. Existing tests either assume a constant out-of-sample forecast performance or use non-parametric techniques robust to time-variation; consequently, they may lack power against state-dependent predictability. Our tests can be applied to relative forecast comparisons, forecast encompassing, forecast efficiency, and, more generally, moment-based tests of forecast evaluation. Monte Carlo results suggest that our proposed tests perform well in finite samples and have better power than existing tests in selecting the best forecast or assessing its efficiency in the presence of state dependence. Our tests uncover "pockets of predictability" in U.S. equity premia; although the term spread is not a useful predictor on average over the sample, it forecasts significantly better than the benchmark forecast when real GDP growth is low. In addition, we find that leading indicators, such as measures of vacancy postings and new orders for durable goods, improve the forecasts of U.S. industrial production when financial conditions are tight.