Qu.test: Qu test for true long memory against spurious long memory.
In FunWithR/LongMemoryTS: Long Memory Time Series

Description Usage Arguments References Examples

Qu.test Test statistic of Qu (2011) for the null hypotesis of true long memory against the alternative of spurious long memory.

1	Qu.test(data, m, epsilon = 0.05)

`data`	data vector of length T.
`m`	bandwith parameter specifying the number of Fourier frequencies used for the estimation usually `floor(1+T^delta)`, where 0.5<delta<0.8 for consistency.
`epsilon`	trimming parameter `epsilon=0.05` by default. Determines minimum number of Fourier frequencies used in test statistic. For T>500 it is recommended to use `epsilon=0.02`.Confer Qu (2011) for further details.

Qu, Z. (2011): A Test Against Spurious Long Memory. Journal of Business and Economic Statistics, Vol. 29, No. 3, pp. 423 - 438.

library(fracdiff)
T<-500
m<-floor(1+T^0.75)
series<-fracdiff.sim(n=T,d=0.4)$series
shift.series<-ARRLS.sim(T=500,phi=0.5, sig.shift=0.75, prob=5/T, sig.noise=1)
ts.plot(series, ylim=c(min(min(series),min(shift.series)),max(max(series),max(shift.series))))
lines(shift.series, col=2)
Qu.test(series,m=m, epsilon=0.05)
Qu.test(shift.series,m=m, epsilon=0.05)