Nonparametric risk bounds for time-series forecasting

Generalization error bounds are probabilistically valid, non-asymptotic tools for characterizing the predictive ability of forecasting models. This methodology is fundamentally about choosing particular prediction functions out of some class of plausible alternatives so that, with high reliability, the resulting predictions will be nearly as accurate as possible ("probably approximately correct"). While many of these results are aimed at classification problems with independent and identically distributed (i.i.d.) data, this paper adapts and extends these methods to time-series models, so that economic and financial forecasting techniques can be evaluated rigorously. In particular, these methods control the expected accuracy of future predictions from mis-specified models based on finite samples. This allows for immediate model comparisons which neither appeal to asymptotics nor make strong assumptions about the data-generating process, in stark contrast to such popular model-selection tools as AIC.