The moving blocks bootstrap versus parametric time series models

Abstract

The application of a parametric time series model to a water resources problem involves selecting a model and estimating its parameters, both steps adding uncertainty to the analysis. The moving blocks bootstrap is a simple resampling algorithm which can replace parametric time series models, avoiding model selection and only requiring an estimate of the moving block length. The moving blocks bootstrap resamples the observed time series using approximately independent moving blocks. A Monte Carlo experiment is performed involving the use of a time series model to estimate the storage capacity S of a surface water reservoir. Our results document that the bootstrap always produced storage estimates with lower root‐mean‐square‐error than a parametric alternative, even when no model error is introduced into the parametric scheme. These results suggest that the moving blocks bootstrap can provide a simple and attractive alternative to more complex multivariate ARMA models.