ELW2S function

Two-Step Exact local Whittle estimator of fractional integration with unknown mean and time trend.

ELW2S implements the two-step ELW estimator of Shimotsu (2010) that is consistent and asymptotically normal in the range from -1/2 to 2.

ELW2S(data, m, trend_order = 0, taper = c("Velasco", "HC"))

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.
• trend_order: specifies the form of detrending: 0 for a constant, only, 1 for a linear trend, and so on.
• taper: string from c("Velasco","HC") specifying the tapered form of the local Whittle estimator used in the first step.

Examples

library(fracdiff)
T<-1000
d<-0.8
trend<-(1:T)/T
series<-cumsum(fracdiff.sim(T,d=(d-1))$series)
ts.plot(series)
ELW2S(series, m=floor(1+T^0.7), trend_order=0)$d
series2<-series+2*trend
ELW2S(series2, m=floor(1+T^0.7), trend_order=1)$d
series3<-series+2*trend+2*trend^2
ELW2S(series3, m=floor(1+T^0.7), trend_order=2)$d

References

Shimotsu, K. (2010): Exact Local Whittle Estimation Of Fractional Integration with Unknown Mean and Time Trend. Econometric Theory, Vol. 26, pp. 501 - 540.

Author(s)

Christian Leschinski