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Long memory or shifting means? A new approach and application to realised volatility

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Abstract

It is now recognised that long memory and structural change can be confused because the statistical properties of times series of lengths typical of financial and econometric series are similar for both models. We propose a new set of methods aimed at distinguishing between long memory and structural change. The approach, which utilises the computational efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the fractional integration parameter, d, with regime length for simulated fractionally integrated series. This bivariate distribution is then compared with the data for the time series. We also combine ART with the established goodness of fit test for long memory series due to Beran. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show that in these series the value of the fractional integration parameter is not constant with time. The mathematical consequence of this is that the definition of H self-similarity is violated. We present evidence that these series have structural breaks.

Suggested Citation

  • Eduardo Mendes & Les Oxley & William Rea & Marco Reale, 2008. "Long memory or shifting means? A new approach and application to realised volatility," Working Papers in Economics 08/04, University of Canterbury, Department of Economics and Finance.
  • Handle: RePEc:cbt:econwp:08/04
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    File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/0804.pdf
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    Keywords

    Long-range dependence; Strong dependence; Global dependence; Hurst phenomena;

    JEL classification:

    • 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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