IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i4p1195-1217.html
   My bibliography  Save this article

High-frequency asymptotics for path-dependent functionals of Itô semimartingales

Author

Listed:
  • Duembgen, Moritz
  • Podolskij, Mark

Abstract

The estimation of local characteristics of Itô semimartingales has received a great deal of attention in both academia and industry over the past decades. In various papers limit theorems were derived for functionals of increments and ranges in the infill asymptotics setting. In this paper we establish the asymptotic theory for a wide class of statistics that are built from the incremental process of an Itô semimartingale. More specifically, we will show the law of large numbers and the associated stable central limit theorem for the path dependent functionals in the continuous setting, and discuss the asymptotic theory for range-based statistics in the discontinuous framework. Some examples from economics and physics demonstrate the potential applicability of our theoretical results in practice.

Suggested Citation

  • Duembgen, Moritz & Podolskij, Mark, 2015. "High-frequency asymptotics for path-dependent functionals of Itô semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1195-1217.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1195-1217
    DOI: 10.1016/j.spa.2014.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914002026
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    2. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    3. Kim Christensen & Mark Podolskij, 2012. "Asymptotic Theory of Range-Based Multipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 417-456, June.
    4. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
    5. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    6. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    7. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    8. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liao, Yin & Anderson, Heather M., 2019. "Testing for cojumps in high-frequency financial data: An approach based on first-high-low-last prices," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 252-274.
    2. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    3. Beatriz Vaz de Melo Mendes & Victor Bello Accioly, 2017. "Improving (E)GARCH forecasts with robust realized range measures: Evidence from international markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 41(4), pages 631-658, October.
    4. Charlotte Christiansen, 2010. "Decomposing European bond and equity volatility," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(2), pages 105-122.
    5. Barndorff-Nielsen, Ole E. & Corcuera, José Manuel & Podolskij, Mark, 2009. "Power variation for Gaussian processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1845-1865, June.
    6. Richard Gerlach & Declan Walpole & Chao Wang, 2017. "Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 199-215, February.
    7. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    8. Christensen, Kim & Podolskij, Mark, 2006. "Range-Based Estimation of Quadratic Variation," Technical Reports 2006,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Tan, Shay-Kee & Ng, Kok-Haur & Chan, Jennifer So-Kuen & Mohamed, Ibrahim, 2019. "Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 537-551.
    10. Neda Todorova, 2012. "Volatility estimators based on daily price ranges versus the realized range," Applied Financial Economics, Taylor & Francis Journals, vol. 22(3), pages 215-229, February.
    11. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    12. Korkusuz, Burak & Kambouroudis, Dimos & McMillan, David G., 2023. "Do extreme range estimators improve realized volatility forecasts? Evidence from G7 Stock Markets," Finance Research Letters, Elsevier, vol. 55(PB).
    13. Mark Podolskij & Mathias Vetter, 2009. "Understanding limit theorems for semimartingales: a short survey," CREATES Research Papers 2009-47, Department of Economics and Business Economics, Aarhus University.
    14. Bollerslev, Tim & Li, Jia & Li, Qiyuan, 2024. "Optimal nonparametric range-based volatility estimation," Journal of Econometrics, Elsevier, vol. 238(1).
    15. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    16. Shay Kee Tan & Kok Haur Ng & Jennifer So-Kuen Chan, 2022. "Predicting Returns, Volatilities and Correlations of Stock Indices Using Multivariate Conditional Autoregressive Range and Return Models," Mathematics, MDPI, vol. 11(1), pages 1-24, December.
    17. Bhaumik, S. & Karanasos, M. & Kartsaklas, A., 2016. "The informative role of trading volume in an expanding spot and futures market," Journal of Multinational Financial Management, Elsevier, vol. 35(C), pages 24-40.
    18. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    19. Kim Christensen & Mark Podolskij & Mathias Vetter, 2009. "Bias-correcting the realized range-based variance in the presence of market microstructure noise," Finance and Stochastics, Springer, vol. 13(2), pages 239-268, April.
    20. Mark Podolskij & Nakahiro Yoshida, 2013. "Edgeworth expansion for functionals of continuous diffusion processes," CREATES Research Papers 2013-33, Department of Economics and Business Economics, Aarhus University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1195-1217. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.