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.

A comparison of the power of thettest, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des teststde Student, de Mann-Kendall et du bootstrap pour la détection de tendance

“…Its merit is that it is free of the restrictive assumption regarding normality of sample data, and that the method is easy to understand and implement (Simon & Bruce, 1991). The bootstrap techniques have been applied to resolve various problems in the water resources field as demonstrated by Zucchini & Adamson (1989), Vogel & Shallcross (1996), Lall & Sharma (1996), Tasker & Dunne (1997), Stefano et al (2000) and Yue & Wang (2002). The rank-based bootstrap MK test has also been used to detect trends in hydrological time series (e.g.…”

Bootstrap order selection for SETAR models

“…By inspecting this table, it is possible to see the strong impact of the AN N s on the SET AR performances: averaging over all the DGP s and sample sizes the standard MAICE procedure achieves a correct selection of the process 30.5% of the time whereas our procedure does 40.6 %. In the previous experiment it was 47.4% and 57.9% respectively.…”

“…, m} belong to the j-th block (the performances of these two approaches have investigated in [14] and [19] in terms of the estimation error). For both the procedures, the crucial point is to choose the blocklength so that the dynamic structure of neighbored observations within the blocks is preserved and the data belonging to different blocks are separated far enough in time to show a vanishing autocorrelation structure ( [47]). In more details, in order to achieve consistency ( [14]) for the generic blocklength m = m t the following must be true: m → ∞ and T −1 m → 0 as T → ∞; that is the blocksize m tends to infinity but at a rate slower than the sample size T.…”

Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method

“…Vogel and Shallcross [44] used the moving blocks bootstrap to resample the observed time series of stream flow to estimate the storage capacity of a reservoir with different reliability. In order to evaluate the correlation between evapotranspiration and forest biomass, Jaramillo et al [45] performed a bootstrapping procedure to account for the sampling standard errors of the forest attribute data in the regression analysis.…”