Title: Bootstrapping Generalization Error Bounds for Time Series,
Abstract: We consider the problem of finding confidence intervals for the risk of
forecasting the future of a stationary, ergodic stochastic process, using a
model estimated from the past of the process. We show that a bootstrap
procedure provides valid confidence intervals for the risk, when the data
source is sufficiently mixing, and the loss function and the estimator are
suitably smooth. Autoregressive (AR(d)) models estimated by least squares obey
the necessary regularity conditions, even when mis-specified, and simulations
show that the finite- sample coverage of our bounds quickly converges to the
theoretical, asymptotic level. As an intermediate step, we derive sufficient
conditions for asymptotic independence between empirical distribution functions
formed by splitting a realization of a stochastic process, of independent
interest.