The replacement bootstrap for dependent data

Applications that deal with time-series data often require evaluating complex statistics for which each time series is essentially one data point. When only a few time series are available, bootstrap methods are used to generate additional samples that can be used to evaluate empirically the statistic of interest. In this work a novel bootstrap method is proposed, which is shown to have some asymptotic consistency guarantees under the only assumption that the time series are stationary and ergodic. This contrasts previously available results that impose mixing or finite-memory assumptions on the data. Empirical evaluation on simulated and real data, using a practically relevant and complex extrema statistic is provided.