I know that the series is stationary and has long memory property if the fractional parameter d is between 0 and 0.5. But is it for stationarity or for testing that the series has a long memory? Moreover, if we estimate d by GPH test and the estimated d=0.20, can we say that the series has long memory? I just have doubts if the estimated value of d can be use for stationarity and hypothesis testing as well.
If d is greater than 0 but less than 1 the series is fractionally integrated (and so neither stationary nor integrated). If d
d is the estimated fractional differencing parameter. The null hypothesis is d =1 and the alternative is d < 1(fractional integration) so if d=.20 then d-1 = -.80 and you will need sb (standard error) to formulate a t test, which is t= d-1/sb. A variable is non-stationary when d > or = 0.5.Another way, for 0 < d d>=0.5 nonstationary.
Hi Jane
If you look at Bollerslev, 1996, paper you can get more details on this issue, but in general if d=0, the series is covariance stationary and possess short memory process, whereas in the case of d=1 the series is non-stationary. However, in the case of 0
The series is stationary or say short memory if d lies between -1/2 and 1/2. But if d is strictly between 0 and 1/2, then its long memory.
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