A New Procedure to Test for H Self-Similarity
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 nancial and economic series are similar for both mod- els. We propose a new test aimed at distinguishing between unifractal long memory and structural change. The approach, which utilizes the computationally ecient 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 sig- ni cantly di erent 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.
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- Smith, Aaron, 2005.
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- Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
- 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.
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