Author(s)

William Rea¹, Chris Price², Les Oxley³, Marco Reale², Jennifer Brown²

¹Department of Economics and Finance, University of Canterbury, Christchurch, New Zealand.
²Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
³Waikato Management School, University of Waikato, Hamilton, New Zealand.

It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing between a null hypothesis of unifractal fractionally integrated processes and an alternative hypothesis of other processes which display the long memory property. The procedure is based on a pair of empirical, but consistently defined, statistics namely the number of breaks reported by Atheoretical Regression Trees (ART) and the range of the Empirical Fluctuation Process (EFP) in the CUSUM test. The new procedure 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 which rejects the null hypothesis for a candidate series if its pair of statistics lies on the periphery of the bivariate distribution determined from simulation under the null. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average and show that the rejection rate of the null is higher than if either statistic was used as a univariate test.

Long-Range Dependence, Strong Dependence, Global Dependence, Regression Trees, CUSUM Test, Volatility

Rea, W. , Price, C. , Oxley, L. , Reale, M. and Brown, J. (2016) A New Procedure to Test for Fractional Integration. Open Journal of Statistics, 6, 651-666. doi: 10.4236/ojs.2016.64055.