Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps
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Date
2013-05-15
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Abstract
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations
which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from
Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under
non-synchronous observations, we derive a stable central limit theorem for the estimator by Hayashi
and Yoshida (2005) in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps
affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly
discussed.
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Keywords
asynchronous observations, co-jumps, quadratic covariation, statistics of semimartingales