Limit theorems for multipower variation in the presence of jumps. (English) Zbl 1096.60022

This paper deals with a systematic study of how the probability limit and central limit theorem for realised multipower variation changes when we add finite activity jump processes to an underlying Brownian semimartingale.


60G44 Martingales with continuous parameter
60F05 Central limit and other weak theorems
Full Text: DOI Link


[1] O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: Y. Kabanov, R. Lipster, J. Stoyanov (Eds.), From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006 (in press) · Zbl 1106.60037
[2] O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, N. Shephard, Limit theorems for realised bipower variation in econometrics, Econometric Theory 22 (2006) (in press) · Zbl 1125.62114
[3] Barndorff-Nielsen, O.E.; Shephard, N., Realised power variation and stochastic volatility, Bernoulli, 9, 243-265, (2003), Correction published in pages 1109-1111 · Zbl 1026.60054
[4] Barndorff-Nielsen, O.E.; Shephard, N., Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics, Econometrica, 72, 885-925, (2004) · Zbl 1141.91634
[5] Barndorff-Nielsen, O.E.; Shephard, N., Power and bipower variation with stochastic volatility and jumps (with discussion), Journal of financial econometrics, 2, 1-48, (2004)
[6] Barndorff-Nielsen, O.E.; Shephard, N., Econometrics of testing for jumps in financial economics using bipower variation, Journal of financial econometrics, 4, 1-30, (2006)
[7] Bertoin, J., Lévy processes, (1996), Cambridge University Press Cambridge · Zbl 0861.60003
[8] Blumenthal, R.M.; Getoor, R.K., Sample functions of stochastic processes with independent increments, Indiana university mathematics journal, 10, 493-516, (1961) · Zbl 0097.33703
[9] Jacod, J.; Protter, P., Asymptotic error distributions for the Euler method for stochastic differential equations, Annals of probability, 26, 267-307, (1998) · Zbl 0937.60060
[10] Revuz, D.; Yor, M., Continuous martingales and Brownian motion, (1999), Springer-Verlag Heidelberg · Zbl 0917.60006
[11] Sato, K., Lévy processes and infinitely divisible distributions, (1999), Cambridge University Press Cambridge · Zbl 0973.60001
[12] M. Winkel, Explicit constructions of Monroe’s embedding and a converse for Lévy processes, Department of Statistics, University of Oxford, 2005 (unpublished paper)
[13] Woerner, J., Power and multipower variation: inference for high frequency data, (), 343-364 · Zbl 1142.62095
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.