Journal of Econometrics 198 (2017) 10–28
Contents lists available at ScienceDirect
Journal of Econometrics
journal homepage: ate/jeconom
A local stable bootstrap for power variations of pure-jump
semimartingales and activity index estimation✩
Ulrich Hounyo a,b, Rasmus T. Varneskov c,b,d,∗
a Department of Economics and Business Economics, Aarhus University, Denmark
b CREATES, Aarhus University, Denmark
c Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, United States
d Nordea Asset Management, Sweden
a r t i c l e i n f o a b s t r a c t
Article history: We provide a new resampling procedure – the local stable bootstrap – that is able to mimic the
Received 30 January 2016 dependence properties of realized power variations for pure-jump semimartingales observed at different
Received in revised form frequencies. This allows us to propose a bootstrap estimator and inference procedure for the activity index
13 August 2016 of the underlying process, β, as well as bootstrap tests for whether it obeys a jump-diffusion or a pure-
Accepted 7 January 2017
jump process, that is, of the null hypothesis : β= 2 against the alternative : β< 2. We establish
Available online 20 January 2017 H0 H1
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
JEL classification: H0
C12 tests pared to those of benchmark tests using Monte Carlo simulations. Unlike existing procedures,
C14 our bootstrap tests are correctly sized in general settings. Finally, we illustrate the use and properties of
C15 the new bootstrap diffusion tests using high-frequency data on three FX series, the S&P 500, and the VIX.
G1 © 2017 Elsevier . All rights reserved.
Keywords:
Activity index
Bootstrap
Blumenthal–Getoor index
Confidence intervals
High-frequency data
Hypothesis t
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