A wavelet analysis of scaling laws and long-memory in stock market volatility
AbstractThis paper investigates the dependence of average stock market volatility on the timescale or on the time interval used to measure price changes, which dependence is often referred to as the scaling law. Scaling factor, on the other hand, refers to the elasticity of the volatility measure with respect to the timescale. This paper studies, in particular, whether the scaling factor differs from the one in a simple random walk model and whether it has remained stable over time. It also explores possible underlying reasons for the observed behaviour of volatility in terms of heterogeneity of stock market players and periodicity of in-traday volatility. The data consist of volatility series of Nokia Oyj at the Helsinki Stock Exchange at five minute frequency over the period from January 4, 1999 to December 30, 2002. The paper uses wavelet methods to decompose stock market volatility at different timescales. Wavelet methods are particularly well motivated in the present context due to their superior ability to describe local properties of times se-ries. The results are, in general, consistent with multiscaling in Finnish stock markets. Furthermore, the scaling factor and the long-memory parameters of the volatility series are not constant over time, nor con-sistent with a random walk model. Interestingly, the evidence also suggests that, for a significant part, the behaviour of volatility is accounted for by an intraday volatility cycle referred to as the New York effect. Long-memory features emerge more clearly in the data over the period around the burst of the IT bubble and may, consequently, be an indication of irrational exuberance on the part of investors.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Bank of Finland in its series Research Discussion Papers with number 27/2005.
Length: 44 pages
Date of creation: 11 Oct 2005
Date of revision:
long-memory; scaling; stock market; volatility; wavelets;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-21 (All new papers)
- NEP-ECM-2006-10-21 (Econometrics)
- NEP-ETS-2006-10-21 (Econometric Time Series)
- NEP-FMK-2006-10-21 (Financial Markets)
- NEP-MST-2006-10-21 (Market Microstructure)
- NEP-RMG-2006-10-21 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Patrick M. Crowley, 2005.
"An intuitive guide to wavelets for economists,"
GE, Growth, Math methods
- Andersen, Torben G & Bollerslev, Tim, 1997.
" Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns,"
Journal of Finance,
American Finance Association, vol. 52(3), pages 975-1005, July.
- Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc.
- U. A. Muller & M. M. Dacorogna & R. D. Dave & O. V. Pictet & R. B. Olsen & J.R. Ward, . "Fractals and Intrinsic Time - a Challenge to Econometricians," Working Papers 1993-08-16, Olsen and Associates.
- Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
- Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
- Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon, 2001. "Differentiating intraday seasonalities through wavelet multi-scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 543-556.
- Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
- Mark J. Jensen, 1997.
"Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter,"
- Jensen, Mark J, 1999. "Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter," MPRA Paper 39152, University Library of Munich, Germany.
- Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Working Papers 02-3, Bank of Canada.
- Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
- Tkacz, Greg, 2000.
"Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator,"
00-5, Bank of Canada.
- Tkacz Greg, 2001. "Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(1), pages 1-15, April.
- Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
- Jensen, Mark J., 2000.
"An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 24(3), pages 361-387, March.
- Mark J. Jensen, 1997. "An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets," Econometrics 9709002, EconWPA.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
- Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon, 2001. "Scaling properties of foreign exchange volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 249-266.
- Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1995. "Multivariate Stochastic Variance Models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4783, Universidad Carlos III de Madrid.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Torben G. Andersen & Tim Bollerslev, 1998. "Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies," Journal of Finance, American Finance Association, vol. 53(1), pages 219-265, 02.
- Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
- Silvo Dajčman, 2013. "Interdependence Between Some Major European Stock Markets - A Wavelet Lead/Lag Analysis," Prague Economic Papers, University of Economics, Prague, vol. 2013(1), pages 28-49.
- Roger Bowden & Jennifer Zhu, 2010. "Multi-scale variation, path risk and long-term portfolio management," Quantitative Finance, Taylor and Francis Journals, vol. 10(7), pages 783-796.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Minna Nyman).
If references are entirely missing, you can add them using this form.