Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
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Jeannette H. C. Woerner
Summary
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 Lévy processes, estimates for integrals with respect to Lévy measures and non-parametric estimation for Lévy processes will be derived and viewed in the framework of variational sums.
© 2003 Oldenbourg Wissenschaftsverlag GmbH
Articles in the same Issue
- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
Articles in the same Issue
- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
