IDEAS home Printed from https://ideas.repec.org/a/bes/jnlbes/v28i2y2010p275-290.html
   My bibliography  Save this article

Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices

Author

Listed:
  • Perron, Pierre
  • Qu, Zhongjun

Abstract

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.)

Suggested Citation

  • Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
  • Handle: RePEc:bes:jnlbes:v:28:i:2:y:2010:p:275-290
    as

    Download full text from publisher

    File URL: http://pubs.amstat.org/doi/abs/10.1198/jbes.2009.06171
    File Function: full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    2. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
    3. 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 261-268, July.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
    6. 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.
    7. 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.
    8. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
    9. 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.
    10. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, October.
    11. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    12. 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.
    13. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    14. 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.
    15. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    16. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    17. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    18. 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.
    19. 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.
    20. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    21. 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.
    22. 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.
    23. 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.
    24. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    25. repec:adr:anecst:y:1995:i:40:p:04 is not listed on IDEAS
    26. Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January.
    27. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    28. 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(4), pages 686-710, August.
    29. 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.
    30. Zhongjun Qu & Pierre Perron, 2008. "A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and NASDAQ Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-007, Boston University - Department of Economics.
    31. Vadim Teverovsky & Murad Taqqu, 1997. "Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(3), pages 279-304, May.
    32. Iliyan GEORGIEV, 2002. "Functional Weak Limit Theory for Rare Outlying Events," Economics Working Papers ECO2002/22, European University Institute.
    33. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, October.
    34. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    35. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
    36. Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, University Library of Munich, Germany.
    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. 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.
    2. 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.
    3. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
    4. Gary Biglaiser & Ching-to Albert Ma, 2007. "Moonlighting: public service and private practice," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1113-1133, December.
    5. Abderrazak Ben Maatoug & Rim Lamouchi & Russell Davidson & Ibrahim Fatnassi, 2018. "Modelling Foreign Exchange Realized Volatility Using High Frequency Data: Long Memory versus Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(1), pages 1-25, March.
    6. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    7. Xu, Jiawen & Perron, Pierre, 2014. "Forecasting return volatility: Level shifts with varying jump probability and mean reversion," International Journal of Forecasting, Elsevier, vol. 30(3), pages 449-463.
    8. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    9. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    10. 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.
    11. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    12. Andrés Herrera Aramburú & Gabriel Rodríguez, 2016. "Volatility of stock market and exchange rate returns in Peru: Long memory or short memory with level shifts?," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 9(1), pages 45-66.
    13. Rasmus T. Varneskov & Pierre Perron, 2018. "Combining long memory and level shifts in modelling and forecasting the volatility of asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 371-393, March.
    14. Maheu John, 2005. "Can GARCH Models Capture Long-Range Dependence?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-43, December.
    15. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    16. Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.
    17. Zhongjun Qu & Pierre Perron, 2008. "A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and NASDAQ Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-007, Boston University - Department of Economics.
    18. Pierre Perron & Wendong Shi, 2020. "Temporal Aggregation and Long Memory for Asset Price Volatility," JRFM, MDPI, vol. 13(8), pages 1-18, August.
    19. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    20. Scharth, Marcel & Medeiros, Marcelo C., 2009. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," International Journal of Forecasting, Elsevier, vol. 25(2), pages 304-327.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    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: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: . General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    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: Christopher F. Baum (email available below). General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.