ELW function

Exact local Whittle estimator of the fractional difference parameter d for stationary and non-stationary long memory.

ELW implements the exact local Whittle estimator of Shimotsu and Phillips (2005) that is consistent and asymptotically normal as long as the optimization range is less than 9/2, so that it is possible to estimate the memory of stationary as well as non-stationary processes.

ELW(data, m, mean.est = c("mean", "init", "weighted", "none"))

Arguments

• 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<delta<1.
• mean.est: specifies the form of mean correction. One of c("mean","init","weighted","none").

Examples

library(fracdiff)
T<-1000
d<-0.8
series<-cumsum(fracdiff.sim(T,d=(d-1))$series)
ts.plot(series)
ELW(series, m=floor(1+T^0.7))$d

References

Shimotsu, K. and Phillips, P. C. B. (2005): Exact Local Whittle Estimation Of Fractional Integration. The Annals of Statistics, Vol. 33, No. 4, pp. 1890 - 1933

Author(s)

Christian Leschinski