Jeannette H.C. Woerner
In the framework of general semimartingale models we provide limit theorems for
variational sums including the p-th power variation, i.e. the sum of p-th absolute powers of increments of a process. This gives new insight in the use
of quadratic and realised power variation as an estimate for the integrated
volatility in finance. It also provides a criterion to decide from high frequency data, whether a jump component should be included in the model.
Furthermore, results on the asymptotic behaviour of integrals with respect to
Levy processes, estimates for integrals with respect to Levy measures and non-parametric estimation for Levy processes will be derived and viewed in the
framework of variational sums.
Published in Statistics & Decisions 21, 47-68 (2003)
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