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Long memory in volatilities of German stock returns

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  • Philipp Sibbertsen

Abstract

We show that there is strong evidence of long-range dependence in the volatilities of several German stock returns. This will be done by applying a method using the difference of the classical log-periodogram regression estimator for the memory parameter and of the tapered periodogram based estimator. Both estimators give similar values for the memory parameter for each series and this indicates long memory. To support our findings we apply also a methodology using the sample variance and a wavelet based estimator to the data. Also these two methods show clear evidence of long-range dependence in the volatilities of German stock returns. Copyright Springer-Verlag 2004

Suggested Citation

  • Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, September.
    • Handle: RePEc:spr:empeco:v:29:y:2004:i:3:p:477-488
    DOI: 10.1007/s00181-003-0179-z
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    References listed on IDEAS

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    1. 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.
    2. Krämer, Walter & Sibbertsen, Philipp & Kleiber, Christian, 2001. "Long memory vs. structural change in financial time series," Technical Reports 2001,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    4. Walter Kramer & Philipp Sibbertsen, 2002. "Testing for Structural Changes in the Presence of Long Memory," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 1(3), pages 235-242, December.
    5. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    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.
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    8. 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.
    9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    10. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    11. Sibbertsen, Philipp, 2003. "Log-periodogram estimation of the memory parameter of a long-memory process under trend," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 261-268, February.
    12. Clifford M. Hurvich & Rohit S. Deo, 1999. "Plug‐in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 331-341, May.
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    More about this item

    Keywords

    Long memory; volatilities; log-periodogram estimation; C14; C22;
    All these keywords.

    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; Diffusion Processes

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