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

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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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider41
StatusUdgivet - 1 jun. 2015
SerietitelCREATES Research Papers


  • Activity index, Bootstrap, Blumenthal-Getoor index, Confidence Intervals, Highfrequency Data, Hypothesis Testing, Realized Power Variation, Stable Processes

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