multiwave (version 1.0)

vfracdiff: simulation of vectorial fractional differencing process

Description

Given a vectorial process x and a vector of long memory parameters d, this function is producing the corresponding fractional differencing process.

Usage

vfracdiff(x, d)

Arguments

x

initial process.

d

vector of long-memory parameters

Value

vectorial fractional differencing of x.

Details

Given a process x, this function applied a fractional difference procedure using the formula: $$ diag((1-L)^d) x,$$

where L is the lag operator.

References

S. Achard, I. Gannaz (2014) Multivariate wavelet Whittle estimation in long-range dependence. arXiv, http://arxiv.org/abs/1412.0391

K. Shimotsu (2007) Gaussian semiparametric estimation of multivariate fractionally integrated processes Journal of Econometrics Vol. 137, N. 2, pages 277-310.

See Also

varma, varfima

Examples

rho1 <- 0.3
rho2 <- 0.8
cov <- matrix(c(1,rho1,rho2,rho1,1,rho1,rho2,rho1,1),3,3)
d <- c(0.2,0.3,0.4)


J <- 9
N <- 2^J
VMA <- diag(c(0.4,0.1,0))
### or another example VAR <- array(c(0.8,0,0,0,0.6,0,0,0,0.2,0,0,0,0,0.4,0,0,0,0.5),dim=c(3,3,2))
VAR <- diag(c(0.8,0.6,0))
x <- varma(N, k=3, cov_matrix=cov, VAR=VAR, VMA=VMA)
vx<-vfracdiff(x,d)