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

Ulrich Hounyo, Rasmus T. Varneskov*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskriftTidsskriftartikelpeer review

Abstrakt

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, , as well as bootstrap tests for whether it obeys a jump-diffusion or a pure-jump process, that is, of the null hypothesis against the alternative . We establish first-order asymptotic validity of the resulting bootstrap power variations, activity index estimator, and diffusion tests for . Moreover, the finite sample size and power properties of the proposed diffusion tests are compared to those of benchmark tests using Monte Carlo simulations. Unlike existing procedures, our bootstrap tests are correctly sized in general settings. Finally, we illustrate the use and properties of the new bootstrap diffusion tests using high-frequency data on three FX series, the S&P 500, and the VIX.
OriginalsprogEngelsk
Artikelnummer102135
TidsskriftJournal of Econometrics
Vol/bind198
Udgave nummer1
Sider (fra-til)10-28
Antal sider19
ISSN0304-4076
DOI
StatusUdgivet - maj 2017
Udgivet eksterntJa

Emneord

  • Activity index
  • Bootstrap
  • Blumenthal–Getoor index
  • Confidence intervals
  • High-frequency data
  • Hypothesis testing
  • Realized power variation
  • Stable processes

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