## 統計数学セミナー

担当者 吉田朋広、荻原哲平、小池祐太 http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

### 2008年02月06日(水)

14:50-16:00   数理科学研究科棟(駒場) 056号室
Jean JACOD 氏 (Universite Paris 6)
Estimating the Degree of Activity of jumps in High Frequency Data
[ 講演概要 ]
Suppose that a continuous-time process X = (X_t )_{t >= 0} is observed at finitely many times, regularly spaced, on the fixed time interval [0, T ]. We suppose that this process is an It\\^o semimartingale, with a non-vanishing diffusion coefficient, and with jumps. The aim is to estimate the so-called ”Blumenthal-Getoor” index of the (partially observed) path on [0, T ], which is the (random) infimum of all reals r such that the sum \\sum_{s\\le T} |\\Delta X_s|^r is finite (\\Delta X_s denotes the jump size at time s). When X is a L'evy process, this infimum is non-random, and also independent of T , and has been introduced by Blumenthal and Getoor. Under appropriate assumptions, unfortunately rather restrictive, we provide an estimator, which is consistent when the step size between observations goes to 0, and satisfies in addition a Central Limit Theorem. We also show the (surprising) values that this estimator takes, when applied to real financial data.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/18.html