## Abstract

In a recent paper [6], we derived a rate efficient (and in some cases variance efficient) estimator for the integrated volatility of the diffusion coefficient of a process in presence of infinite variation jumps. The estimation is based on discrete observations of the process on a fixed time interval with asymptotically shrinking equidistant observation grid. The result in [6] is derived under the assumption that the jump part of the discretely-observed process has a finite variation component plus a stochastic integral with respect to a stable-like Lévy process with index β > 1. Here we show that the procedure of [6] can be extended to accommodate the case when the jumps are a mixture of finitely many integrals with respect to stable-like Lévy processes with indices β_{1} > … ≥ β_{M} ≥ 1.

Original language | English (US) |
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Title of host publication | The Fascination of Probability, Statistics and their Applications |

Subtitle of host publication | In Honour of Ole E. Barndorff-Nielsen |

Publisher | Springer International Publishing |

Pages | 317-341 |

Number of pages | 25 |

ISBN (Electronic) | 9783319258263 |

ISBN (Print) | 9783319258249 |

DOIs | |

State | Published - Jan 1 2015 |

## Keywords

- Central limit theorem
- Integrated volatility
- Itô semimartingale
- Jump activity
- Jumps
- Quadratic variation
- Stable process

## ASJC Scopus subject areas

- Mathematics(all)