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 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 significantly different from fractionally integrated series with the same estimated d value. We present evidence that these series have structural breaks. For comparison purposes we present the results of tests by Zhang and Ohanissian, Russell, and Tsay for these series.