Time series forecasting: model evaluation and selection using nonparametric risk bounds

We derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for traditional time series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These bounds allow forecasters to select among competing models and to guarantee that with high probability, their chosen model will perform well without making strong assumptions about the data generating process or appealing to asymptotic theory. We motivate our techniques with and apply them to standard economic and financial forecasting tools — a GARCHmodel for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification.