jump occurring at time j/n has a larger effect on the component n-1 £г=-1)r- S^(Xi/n) if there
are many observations in the neighborhood of Xjj∕n.
However, since our test is carried over a fixed time span, we can pretest for the presence of
no jumps, following for example Barndorff-Nielsen and Shephard (2004c,d); they proposed a test
based on the properly scaled difference between realized volatility and bipower variation, which is a
consistent estimator of integrated volatility in the presence of large and rare jumps in the log price
process. If the null hypothesis is not rejected, we can apply our methodology. Huang and Tauchen
(2004) also suggest a variety of Hausman type tests for jumps and find evidence of a relatively small
number of jumps in the log price process. A similar finding is reported by Andersen, Bollerslev and
Diebold (2003).
As for the presence of microstructure effects, suppose that the observed price of an asset can
be decomposed into
Xj /m Yj /m + c j/m.
Here Cj/m is interpreted as a noise capturing the market microstructure effect. The contribution
of the microstructure noise on realized volatility has already been analyzed in a series of recent
papers (see e.g. Alt-Sahalia, Mykland and Zhang, 2003, Zhang, Mykland and Alt-Sahalia, 2003,
Bandi and Russell, 2003 and Hansen and Lunde, 2004). For example, if the microstructure noise
has a constant variance, i.e. independent of the sampling interval, then
m-1 RVm,r -p→ 2rν
where ν denotes the variance of the microstructure noise (see Zhang, Mykland and Alt-Sahalia,
2003). As for n-1 £∣=n1-1)r- Sn(Xi/n), due to the discreteness of the measurement error component,
the behavior of (nξn)-1 £n-ι1 1 {∣Xj∕n-Xi∕n∣<ξn} is not easy to assess. Therefore, our procedure will
not be valid if the log price process is contaminated by microstructure noise.
Similarly to the case of large and rare jumps, it is possible to pretest the series under inves-
tigation for the absence of microstructure noise. In fact, Awartani, Corradi and Distaso (2004)
have suggested a simple test for the null hypothesis of no market microstructure, based on the
appropriate scaled difference between two realized volatility measures constructed over different
sampling frequencies.11 We can then apply our procedure over a time span for which neither the
null hypothesis of no jumps nor the null hypothesis of no microstructure noise has been rejected.
11Awartani, Corradi and Distaso (2004) also propose a specification test of the null hypothesis of microstructure
noise with constant variance. See also Barndorff-Nielsen and Shephard (2004c) for an alternative model of the market
microstructure noise, where the variance of the noise is allowed to depend on the sampling frequency of the data.
12