Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices
Recently, there has been an upsurge of interest in the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from zero and the autocovariance function exhibits a slow rate of decay, akin to a long memory process. Partly based on results in Perron and Qu (2007), we analyze the properties of the autocorrelation function, the periodogram and the log periodogram estimate of the memory parameter when the level shift component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. We confront our theoretical predictions using log-squared returns as a proxy for the volatility of some assets returns, including daily S&P 500 returns over the period 1928-2002. The autocorrelations and the path of the log periodogram estimates follow patterns that would obtain if the true underlying process was one of short-memory contaminated by level shifts instead of a fractionally integrated process. A simple testing procedure is also proposed, which reinforces this conclusion.
(This abstract was borrowed from another version of this item.)
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 28 (2010)
Issue (Month): 2 ()
|Contact details of provider:|| Web page: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main|
|Order Information:||Web: http://www.amstat.org/publications/index.html|
References listed on IDEAS
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.:
- Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004.
"Estimating Long Memory in Volatility,"
- Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Jonathan H. Wright, 2000.
"Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns,"
International Finance Discussion Papers
685, Board of Governors of the Federal Reserve System (U.S.).
- Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 397-417.
- Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
- 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.
- Phillips, Peter C.B., 2007.
"Unit root log periodogram regression,"
Journal of Econometrics,
Elsevier, vol. 138(1), pages 104-124, May.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003.
"Modeling and Forecasting Realized Volatility,"
Econometric Society, vol. 71(2), pages 579-625, March.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
- Lobato, I.N. & Savin, N.E., 1996.
"Real and Spurious Long Memory Properties of Stock Market Data,"
96-07, University of Iowa, Department of Economics.
- Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-68, July.
- I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
- Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, EconWPA.
- Francis X. Diebold & Atsushi Inoue, 2000.
"Long Memory and Regime Switching,"
NBER Technical Working Papers
0264, National Bureau of Economic Research, Inc.
- Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January.
- Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
- 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.
- Robert F. Engle & Aaron D. Smith, 1999.
"Stochastic Permanent Breaks,"
The Review of Economics and Statistics,
MIT Press, vol. 81(4), pages 553-574, November.
- Engle, Robert F & Smith, Aaron, 1998. "Stochastic Permanent Breaks," University of California at San Diego, Economics Working Paper Series qt99v0s0zx, Department of Economics, UC San Diego.
- Perron, P, 1988.
"The Great Crash, The Oil Price Shock And The Unit Root Hypothesis,"
338, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
- William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
- Lu, Yang K. & Perron, Pierre, 2010.
"Modeling and forecasting stock return volatility using a random level shift model,"
Journal of Empirical Finance,
Elsevier, vol. 17(1), pages 138-156, January.
- Yang K. Lu & Pierre Perron, 2008. "Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model," Boston University - Department of Economics - Working Papers Series wp2008-012, Boston University - Department of Economics.
- Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
- Sun, Yixiao & Phillips, Peter C. B., 2003.
"Nonlinear log-periodogram regression for perturbed fractional processes,"
Journal of Econometrics,
Elsevier, vol. 115(2), pages 355-389, August.
- Yixiao Sun & Peter C.B. Phillips, 2002. "Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes," Cowles Foundation Discussion Papers 1366, Cowles Foundation for Research in Economics, Yale University.
- Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
- Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
When requesting a correction, please mention this item's handle: RePEc:bes:jnlbes:v:28:i:2:y:2010:p:275-290. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.