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.
Highlights
It is widely assumed as a stylized fact that many financial and economic time series exhibit the statistical property of long memory, see, for example, [1]-[4]
We extend the work of [15] to examine, in greater detail, the statistical properties of Atheoretical Regression Trees (ART) [17]-[19] when applied to true long memory processes
For comparison purposes we provide the p-values for the univariate ART and Cumulative Summation (CUSUM) tests
Summary
It is widely assumed as a stylized fact that many financial and economic time series exhibit the statistical property of long memory, see, for example, [1]-[4]. A number of other models, apart from fractional integration, have been proposed to account for the extraordinary persistence of the correlations across time found in long memory series, for example; time series with structural change, Markov switching processes, and non-linear processes among others. The econometrics literature has paid considerable attention to the problem of distinguishing true long memory from structural change in economic or financial time series which exhibit the long memory property because economic and/or financial arguments can be advanced as to why the series studied may have such breaks. [1] confine their study to these two alternatives
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