G.hat {LongMemoryTS}

Estimation of G matrix for multivariate long memory processes.

Description

G.hat Estimates the matrix G of a multivariate long memory process based on an estimate of the vector of memory parameters. The assumed spectral density is that of Shimotsu (2007).

Usage

G.hat(X, d, m)

Arguments

X

data matrix with T observations of q-dimensional process.

d

q-dimensional data vector.

m

bandwith parameter specifying the number of Fourier frequencies. used for the estimation usually floor(1+T^delta), where 0<delta<1.

References

Shimotsu, K. (2007): Gaussian semiparametric estimation of multivariate fractionally integrated processes. Journal of Econometrics, Vol. 137, No. 2, pp. 277 - 310.

Examples

T<-500
d1<-0.4
d2<-0.2
data<-FI.sim(T, q=2, rho=0, d=c(d1,d2))
G.hat(X=data, d=c(d1,d2), m=floor(1+T^0.6))
#diagonal elements should equal 1/(2*pi)