A nearest neighbor bootstrap for resampling hydrologic time series

Abstract

A nonparametric method for resampling scalar or vector-valued time series is introduced. Multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed. The motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping (resampling it with replacement). The method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form (e.g., linear or nonlinear) of dependence and the form of the probability density function (e.g., Gaussian). Such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data. Connections of the nearest neighbor bootstrap to Markov processes as well as its utility in a general Monte Carlo setting are discussed. Applications to resampling monthly streamflow and some synthetic data are presented. The method is shown to be effective with time series generated by linear and nonlinear autoregressive models. The utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated.