Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.10

Online
ISSN
1941-1928
See all formats and pricing
More options …

Monitoring the Intraday Volatility Pattern

Robertas Gabrys
  • Department of Information and Operations Management, Marshall School of Business, University of Southern California, Los Angeles, CA, USA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Siegfried Hörmann
  • Corresponding author
  • Department of Mathematics, Université Libre de Bruxelles, CP 210 Bd. du Triomphe, Brussels 1050, Belgium
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Piotr Kokoszka
Published Online: 2013-07-26 | DOI: https://doi.org/10.1515/jtse-2012-0006

Abstract

A functional time series consists of curves, typically one curve per day. The most important parameter of such a series is the mean curve. We propose two methods of detecting a change in the mean function of a functional time series. The change is detected on line, as new functional observations arrive. The general methodology is motivated by, and applied to, the detection of a change in the mean intraday volatility pattern. The methodology is asymptotically justified by applying a new notion of weak dependence for functional time series. It is calibrated and validated by simulations based on real intraday volatility curves.

Keywords: change point detection; intraday volatility; functional data analysis; sequential analysis

References

  • Admati, A. R., and P. Pfeiderer. 1988. “A Theory of Intraday Patters: Volume and Price Variability.” The Review of Financial Studies 1:3–40.CrossrefGoogle Scholar

  • Andersen, T. G., and T. Bollerslev. 1997a. “Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long Run in High Frequency Data.” Journal of Finance 52:975–1005.CrossrefGoogle Scholar

  • Andersen, T. G., and T. Bollerslev. 1997b. “Intraday Periodicity and Volatility Persistence in Financial Markets.” Journal of Empirical Finance 2–3:115–58.Google Scholar

  • Andersen, T. G., and T. Bollerslev. 1998. “DM–Dollar Volatility: Intraday Activity Patters, Microeconomic Announcements, and Longer Run Dependencies.” Journal of Finance 53:219–65.CrossrefGoogle Scholar

  • Andersen, T. G., T. Bollerslev, and A. Das. 2001. “Variance-Ratio Statistics and High-Frequency Data: Testing for Changes in Intraday Volatility Patterns.” Journal of Finance 56:305–27.CrossrefGoogle Scholar

  • Andreou, E., and E. Ghysels. 2009. “Structural Breaks in Financial Time Series.” In Handbook of Financial Time Series, edited by T. G. Andersen, R. A. Davis, J-P. Kreiss, and T. Mikosch, 839–70. Berlin Heidelberg: Springer.Google Scholar

  • Aue, A., L. Horváth, M. Hušková, and P. Kokoszka. 2006. “Change–Point Monitoring in Linear Models with Conditionally Heteroskedastic Errors.” Econometrics Journal 9:373–403.Google Scholar

  • Becker, K. G., J. E. Finnerty, and K. J. Kopecky. 1993. “Economic News and Intradaily Volatility in International Bond Markets.” Financial Analyst Journal 49:81–6.Google Scholar

  • Berkes, I., S. Hörmann, and J. Schauer. 2010. “Split Invariance Principles for Stationary Processes.” The Annals of Probability 39:2441–2473.Web of ScienceGoogle Scholar

  • Berkes, I., L. Horváth, P. Kokoszka, and Q.-M. Shao. 2006. “On Discriminating between Long-Range Dependence and Changes in Mean.” The Annals of Statistics 34:1140–65.CrossrefGoogle Scholar

  • de Boor, C. 1991. “B(asic)-Spline Basics.” In Fundamental Developments of Computer-Aided Geometric Modeling, edited by Les Piegl, 27–49. London: Academic Press.Google Scholar

  • Bosq, D. 2000. Linear Processes in Function Spaces. New York: Springer.Google Scholar

  • Chu, C.-S. J., M. Stinchcombe, and H. White. 1996. “Monitoring Structural Change.” Econometrica 64:1045–65.CrossrefGoogle Scholar

  • Csörgö, M., and P. Révész. 1981. Strong Approximations in Probability and Statistics. New York: Academic Press.Google Scholar

  • Cyree, K. B., M. D. Griffiths, and D. B. Winters. 2004. “An Empirical Examination of the Intraday Volatility in Euro–Dollar Rates.” The Quarterly Review of Economics and Finance 44:44–57.CrossrefGoogle Scholar

  • Ferraty, F., and P. Vieu. 2006. Nonparametric Functional Data Analysis: Theory and Practice. New York: Springer.Google Scholar

  • Gabrys, R., and P. Kokoszka. 2007. “Portmanteau Test of Independence for Functional Observations.” Journal of the American Statistical Association 102:1338–48.Web of ScienceGoogle Scholar

  • Gwilym, O., D. G. McMillan, and A. E. Speight. 1999. “The Intra–Day Relationship between Volatility and Volume in LIFFE Futures Markets.” Applied Financial Economics 9:593–604.Google Scholar

  • Hörmann, S., and P. Kokoszka. 2010. “Weakly Dependent Functional Data.” The Annals of Statistics 38:1845–84.Web of ScienceGoogle Scholar

  • Hörmann, S., and P. Kokoszka. 2012. “Functional Time Series.” Handbook of Statistics 30:157–86.Google Scholar

  • Horváth, L., M. Hušková, P. Kokoszka, and J. Steinebach. 2004. “Monitoring Changes in Linear Models.” Journal of Statistical Planning and Inference 126:225–51.Google Scholar

  • Horváth, L., and P. Kokoszka. 2012. Inference for Functional Data with Applications. New York: Springer.Google Scholar

  • Horváth, L., P. Kokoszka, and A. Zhang. 2006. “Monitoring Constancy of Variance in Conditionally Heteroskedastic Time Series.” Econometric Theory 22:373–402.Google Scholar

  • Hughes, M. P., S. D. Smith, and D. B. Winters. 2007. “An Empirical Examination of Intraday Volatility in on–the–Run U.S. Treasury Bills.” Journal of Economics and Business 59:487–99.CrossrefGoogle Scholar

  • Kargin, V., and A. Onatski. 2008. “Curve Forecasting by Functional Autoregression.” Journal of Multivariate Analysis 99:2508–26.Web of ScienceGoogle Scholar

  • Leisch, F., K. Hornik, and C.-M. Kuan. 2000. “Monitoring Structural Changes with the Generalized Fluctuation Test.” Econometric Theory 16:835–45.CrossrefGoogle Scholar

  • Ljung, G., and G. Box. 1978. “On a Measure of Lack of Fit in Time Series Models.” Biometrika 66:67–72.Google Scholar

  • McMillan, D. G., and E. H. Speight. 2006. “Heterogeneous Information Flows and Intra–Day Volatility Dynamic: Evidence from the UK FTSE–100 Stock Index Futures Market.” Applied Financial Economics 16:959–72.Google Scholar

  • Mikosch, T., and C. Stărică. 2002. “Long-Range Dependence Effects and ARCH Modeling.” In Theory and Applications of Long-Range Dependence, Boston, edited by P. Doukhan, G. Oppenheim, and M. S. Taqqu, 439–59. Boston: Birkhäuser.Google Scholar

  • Ramsay, J., G. Hooker, and S. Graves. 2009. Functional Data Analysis with R and MATLAB. New York: Springer.Google Scholar

  • Ramsay, J. O., and B. W. Silverman. 2005. Functional Data Analysis. New York: Springer.Google Scholar

  • Robbins, H. 1970. “Statistical Methods Related to the Law of the Iterated Logarithm.” The Annals of Mathematical Statistics 41:1397–409.CrossrefGoogle Scholar

  • Wang, F., K. Yamazaki, S. Havlin, and E. Stanley. 2006. “Scaling and Memory in Intraday Volatility Return Interval in Stock Market.” Physical Review E 73:026117:1–8.Google Scholar

About the article

Published Online: 2013-07-26


Citation Information: Journal of Time Series Econometrics, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2012-0006.

Export Citation

©2013 by Walter de Gruyter Berlin / Boston. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Brendan K. Beare, Juwon Seo, and Won-Ki Seo
Journal of Time Series Analysis, 2017
[2]
John L. Moran and Patricia J. Solomon
Open Journal of Applied Sciences, 2017, Volume 07, Number 08, Page 385
[3]
Lajos Horváth, Piotr Kokoszka, and Gregory Rice
Journal of Econometrics, 2014, Volume 179, Number 1, Page 66

Comments (0)

Please log in or register to comment.
Log in