Department of Economics and Business Economics

A Local Stable Bootstrap for Power Variations of Pure-Jump Semimartingales and Activity Index Estimation

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  • rp15_26

    Submitted manuscript, 673 KB, PDF document

We provide a new resampling procedure - the local stable bootstrap - that is able to mimic the dependence properties of realized power variations for pure-jump semimartingales observed at different frequencies. This allows us to propose a bootstrap estimator and inference procedure for the activity index of the underlying process, β, as well as a bootstrap test for whether it obeys a jump-diffusion or a pure-jump process, that is, of the null hypothesis H₀: β=2 against the alternative H₁: β<2. We establish first-order asymptotic validity of the resulting bootstrap power variations, activity index estimator, and diffusion test for H0. Moreover, the finite sample size and power properties of the proposed diffusion test are compared to those of benchmark tests using Monte Carlo simulations. Unlike existing procedures, our bootstrap test is correctly sized in general settings. Finally, we illustrate use and properties of the new bootstrap diffusion test using high-frequency data on three FX series, the S&P 500, and the VIX.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages41
Publication statusPublished - 1 Jun 2015
SeriesCREATES Research Papers

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