Wavestrapping time series: Adaptive wavelet-based bootstrapping (Q2712152)

The paper begins with a review of stationary time series models and current approaches for bootstrapping time series followed by basic ideas related to the discrete wavelet transform. Then, the use of the discrete wavelet transform for decorrelating long memory processes as a bootstrapping scheme whose effectiveness is demonstrated via Monte Carlo experiments is presented. As for stationary long memory processes bootstrapping is known not to work properly, the authors introduce ``wavestrapping'' as an adaptive wavelet-based scheme for bootstrapping certain statistics for time series that can be modeled by either long or short memory autocorrelation sequences. Monte Carlo experiments are used to show that wavestrapping works reasonably well in both cases. Examples, including one involving time series related to atmospheric behaviour, are given, and a discussion of open questions and future work is finally presented.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00020].