We derive generalization error bounds 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 n
on-asymptotic bounds need only weak assumptions on the data-generating process, yet allow forecasters to select among competing models and to guarantee, with high probability, that their chosen model will perform well. We motivate our techniques with and apply them to standard economic and financial forecasting tools---a GARCH model 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.
The literature on statistical learning for time series assumes the asymptotic independence or ``mixing of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an
estimator for the $beta$-mixing rate based on a single stationary sample path and show it is $L_1$-risk consistent.
