  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 non-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.
