TITLE:
A New Procedure to Test for Fractional Integration
AUTHORS:
William Rea, Chris Price, Les Oxley, Marco Reale, Jennifer Brown
KEYWORDS:
Long-Range Dependence, Strong Dependence, Global Dependence, Regression Trees, CUSUM Test, Volatility
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.4,
August
23,
2016
ABSTRACT: 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.