IDEAS home Printed from
   My bibliography  Save this paper

Long-Term Dependence Characteristics of European Stock Indices



    (Kent State University)


    (Kent State University)


In this paper we show the degrees of persistence of the time series if eight European stock market indices are measured, after their lack of ergodicity and stationarity has been established. The proper identification of the nature of the persistence of financial time series forms a crucial step in deciding whether econometric modeling of such series might provide meaningful results. Testing for ergodicity and stationarity must be the first step in deciding whether the assumptions of numerous time series models are met. Our results indicate that ergodicity and stationarity are very difficult to establish in daily observations of these market indexes and thus various time-series models cannot be successfully identified. However, the measured degrees of persistence point to the existence of certain dependencies, most likely of a nonlinear nature, which, perhaps can be used in the identification of proper empirical econometric models of such dynamic time paths of the European stock market indexes. The paper computes and analyzes the long- term dependence of the equity index data as measured by global Hurst exponents, which are computed from wavelet multi-resolution analysis. For example, the FTSE turns out to be an ultra-efficient market with abnormally fast mean-reversion, faster than theoretically postulated by a Geometric Brownian Motion. Various methodologies appear to produce non-unique empirical measurement results and it is very difficult to obtain definite conclusions regarding the presence or absence of long term dependence phenomena like persistence or anti-persistence based on the global or homogeneous Hurst exponent. More powerful methods, such as the computation of the multifractal spectra of financial time series may be required. However, the visualization of the wavelet resonance coefficients and their power spectrograms in the form of localized scalograms and average scalegrams, forcefully assist with the detection and measurement of several nonlinear types of market price diffusion.

Suggested Citation

  • Cornelis A. Los & Joanna M. Lipka, 2004. "Long-Term Dependence Characteristics of European Stock Indices," Finance 0409044, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0409044
    Note: Type of Document - pdf. Los, Cornelis A. and Lipka, Joanna M., 'Long-Term Dependence Characteristics of European Stock Indices' (March 2003). Kent State University Department of Finance Working Paper.

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. 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.
    2. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    3. Crato, Nuno & de Lima, Pedro J. F., 1994. "Long-range dependence in the conditional variance of stock returns," Economics Letters, Elsevier, vol. 45(3), pages 281-285.
    4. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    5. Sadique, Shibley & Silvapulle, Param, 2001. "Long-Term Memory in Stock Market Returns: International Evidence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 6(1), pages 59-67, January.
    6. 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.
    7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    8. Mandelbrot, Benoit, 1969. "Long-Run Linearity, Locally Gaussian Process, H-Spectra and Infinite Variances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(1), pages 82-111, February.
    9. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    10. Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Long-Term Dependence; European Stock Indices;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:wpa:wuwpfi:0409044. 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: (EconWPA). General contact details of provider: .

    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 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.

    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.