TFT-bootstrap: Resampling time series in the frequency domain to obtain replicates in the time domain

By Claudia Kirch, Dimitris Nicolas Politis. 2011

86 citations recorded by the source corpus.

A new time series bootstrap scheme, the Time Frequency Toggle (TFT)-Bootstrap, is proposed. Its basic idea is to bootstrap the Fourier coecients of the observed time series, and then back-transforming them to obtain a bootstrap sample in the time domain. Related previous proposals, such as the ‘surrogate data’ approach, resampled only the phase of the Fourier coecients, and thus had only limited validity. By contrast, we show that the appropriate resampling of phase and magnitude in addition to some smoothing of Fourier coecients yields a bootstrap scheme that mimics the correct second-order moment structure for a large class of time series processes. As a main result we obtain a functional limit theorem for the TFT-Bootstrap under a variety of popular ways of frequency domain bootstrapping. Possible applications of the TFT-Bootstrap naturally arise in change-point analysis and unit-root testing where statistics are frequently based on functionals of partial sums. Finally, a small simulation study explores the potential of the TFT-Bootstrap for small samples showing that for the discussed tests in change-point analysis as well as unit-root testing it yields better results than the corresponding asymptotic tests if measured by size and power.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b6453c6d0bdf96528f54f43563d01edad406d5fc

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In Economics and Econometrics

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Citations in the corpus

Change-point detection in panel data via double CUSUM statistic (2016, methodology): “2 Generate a bootstrap sequence of the Fourier coefficients of ξ̂t using the Time Frequency Toggle (TFT)-Bootstrap (Kirch and Politis 2011), to which the inverse fast Fourier transform algorithm is applied to produce ξt.”
On the range of validity of the autoregressive sieve bootstrap (2012, background): “…conjectured that frequency domain bootstrap methods might also be valid without the linearity assumption as long as the statistic in question has a large-sample distribution depending only on first and second order moment properties; cf. Kirch and Politis (2011) for some results in that direction.”