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A New Procedure to Test for H Self-Similarity

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Abstract

It is now recognized that long memory and structural change can be confused because the statistical properties of times series of lengths typical of many financial and economic series are similar for both models. We propose a new test aimed at distinguishing between unifractal long memory and structural change. The approach, which utilizes the computationally efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the number of breaks reported by ART with the CUSUM range for simulated fractionally integrated series. This bivariate distribution is then used to empirically construct a test. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show the realised volatility series are statistically signifcantly different from fractionally integrated series with the same estimated d value. We present evidence that these series have struc- tural breaks. For comparison purposes we present the results of tests by Zhang and Ohanissian, Russell, and Tsay for these series.

Suggested Citation

  • Les Oxley & Chris Price & William Rea & Marco Reale, 2008. "A New Procedure to Test for H Self-Similarity," Working Papers in Economics 08/16, University of Canterbury, Department of Economics and Finance.
  • Handle: RePEc:cbt:econwp:08/16
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    File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/0816.pdf
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    References listed on IDEAS

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    1. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, pages 131-159.
    2. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, pages 465-515.
    3. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics.
    4. Smith, Aaron, 2005. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, pages 321-335.
    5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, pages 131-159.
    6. Jennifer Brown & Les Oxley & William Rea & Marco Reale, 2008. "The Empirical Properties of Some Popular Estimators of Long Memory Processes," Working Papers in Economics 08/13, University of Canterbury, Department of Economics and Finance.
    7. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics.
    8. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, pages 1-34.
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    More about this item

    Keywords

    Long-range dependence; strong dependence; global dependence;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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