Limit theorems for multipower variation in the presence of jumps

In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.

[1]  Lan Zhang.  Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach , 2004, math/0411397.

[2]  N. Shephard,et al.  Econometric analysis of realised volatility and its use in estimating stochastic volatility models , 2000 .

[3]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[4]  S. Delattre,et al.  A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors , 1997 .

[5]  N. Shephard,et al.  Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation , 2005 .

[6]  Jeannette H. C. Woerner.  Power and Multipower Variation: inference for high frequency data , 2006 .

[7]  R. Wolpert.  Lévy Processes , 2000 .

[8]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[9]  Jean Jacod,et al.  Diffusions with measurement errors. I. Local Asymptotic Normality , 2001 .

[10]  P. Hansen,et al.  An Optimal and Unbiased Measure of Realized Variance Based on Intermittent High-Frequency Data , 2003 .

[11]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[12]  Jeffrey R. Russell,et al.  Microstructure noise, realized volatility, and optimal sampling , 2004 .

[13]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[14]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[15]  Jean Jacod,et al.  A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales , 2004 .

[16]  N. Shephard,et al.  LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS , 2005, Econometric Theory.

[17]  P. Protter,et al.  Asymptotic error distributions for the Euler method for stochastic differential equations , 1998 .

[18]  M. Meerschaert.  Regular Variation in R k , 1988 .

[19]  Neil Shephard,et al.  Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise , 2004 .

[20]  N. Shephard,et al.  Realised power variation and stochastic volatility models , 2003 .