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Long range dependence effects and ARCH modelling

Author

Listed:
  • Thomas Mikosch

    (Dept. Actuarial Mathematics, University of Copenhagen)

  • Catalin Starica

    (Dept. Mathematical Statistics & Economics, Gothenburg University & CTH)

Abstract

Our study supports the hypothesis of global non-stationarity of the return time series. We bring forth both theoretical and empirical evidence that the long range dependence (LRD) type behavior of the sample ACF and the periodogram of absolute return series and the IGARCH effect documented in the econometrics literature could be due to the impact of non-stationarity on statistical instruments and estimation procedures. In particular, contrary to the common-hold belief that the LRD characteristic and the IGARCH phenomena carry meaningful information about the price generating process, these so-called stylized facts could be just artifacts due to structural changes in the data. The effect that the switch to a different regime has on the sample ACF and the periodogram is theoretically explained and empirically documented using time series that were the object of LRD modeling efforts (S&P500, DEM/USD FX) in various publications.

Suggested Citation

  • Thomas Mikosch & Catalin Starica, 2004. "Long range dependence effects and ARCH modelling," Econometrics 0412004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0412004
    Note: Type of Document - pdf; pages: 21
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0412/0412004.pdf
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    Citations

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    Cited by:

    1. Andrea Beltratti & Claudio Morana, 2005. "Structural Breaks and Common Factors in the Volatility of the Fama-French Factor Portfolios," ICER Working Papers 23-2005, ICER - International Centre for Economic Research.
    2. Erlandsson, Ulf, 2002. "Regime Switches in Swedish Interest Rates," Working Papers 2002:5, Lund University, Department of Economics, revised 04 Mar 2005.
    3. Ibrahim Ahamada & Jamel Jouini & Mohamed Boutahar, 2004. "Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density," Applied Economics, Taylor & Francis Journals, vol. 36(10), pages 1095-1101.
    4. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    5. Beltratti, A. & Morana, C., 2006. "Breaks and persistency: macroeconomic causes of stock market volatility," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 151-177.
    6. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is what?: A simple time-domain test of long-memory vs. structural breaks," Economics Working Papers 954, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Eric Hillebrand, 2003. "Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models," Econometrics 0301003, University Library of Munich, Germany.
    8. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    9. Cizek, P. & Haerdle, W. & Spokoiny, V., 2007. "Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models," Other publications TiSEM a797e4a8-12cf-4ac5-9fae-b, Tilburg University, School of Economics and Management.
    10. Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 290-318.
    11. Ibrahim Ahamada & Jamel Jouini & Mohamed Boutahar, 2004. "Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density," Applied Economics, Taylor & Francis Journals, vol. 36(10), pages 1095-1101.
    12. Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    13. Morana, Claudio, 2009. "On the macroeconomic causes of exchange rate volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 328-350.
    14. Eric Hillebrand, 2004. "Neglecting Parameter Changes in Autoregressive Models," Departmental Working Papers 2004-04, Department of Economics, Louisiana State University.
    15. Elena Andreou & Eric Ghysels, 2004. "Monitoring for Disruptions in Financial Markets," CIRANO Working Papers 2004s-26, CIRANO.
    16. Lahiani, Amine & Yousfi, Ouidad, 2007. "Modèls Garch à la mémoire longue: application aux taux de change tunisiens [GARCH models : evidence from Tunisian Exchange market]," MPRA Paper 28702, University Library of Munich, Germany, revised 2008.

    More about this item

    Keywords

    sample autocorrelation; change point; GARCH process; long range dependence.;
    All these keywords.

    JEL classification:

    • 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

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