fivarma: simulation of FIVARMA process
In multiwave: Estimation of Multivariate Long-Memory Models Parameters

Description Usage Arguments Details Value Author(s) References See Also Examples

Generates N observations of a realisation of a multivariate FIVARMA process X.

1 2	fivarma(N, d = 0, cov_matrix = diag(length(d)), VAR = NULL, VMA = NULL,skip = 2000)

`N`	number of time points.
`d`	vector of parameters of long-memory.
`cov_matrix`	matrix of correlation between the innovations (optional, default is identity).
`VAR`	array of VAR coefficient matrices (optional).
`VMA`	array of VMA coefficient matrices (optional).
`skip`	number of initial observations omitted, after applying the ARMA operator and the fractional integration (optional, the default is 2000).

Let e(t) be a multivariate gaussian process with a covariance matrix cov_matrix. The values of the process X are given by the equations:

VAR(L)*U(t) = VMA(L)*e(t),

and

diag((1-L)^d)X(t) = U(t)

where L is the lag-operator.

`x`	vector containing the N observations of the vector ARFIMA(arlags, d, malags) process.
`long_run_cov`	matrix of covariance of the spectral density of x around the zero frequency.
`d`	vector of parameters of long-range dependence, modified in case of cointegration.

S. Achard and I. Gannaz

R. J. Sela and C. M. Hurvich (2009) Computationaly efficient methods for two multivariate fractionnaly integrated models. Journal of Time Series Analysis, Vol 30, N. 6, pages 631-651.

S. Achard, I. Gannaz (2016) Multivariate wavelet Whittle estimation in long-range dependence. Journal of Time Series Analysis, Vol 37, N. 4, pages 476-512. http://arxiv.org/abs/1412.0391.

S. Achard, I Gannaz (2019) Wavelet-Based and Fourier-Based Multivariate Whittle Estimation: multiwave. Journal of Statistical Software, Vol 89, N. 6, pages 1-31.

varma, vfracdiff

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))
resp <- fivarma(N, d, cov_matrix=cov, VAR=VAR, VMA=VMA)
x <- resp$x
long_run_cov <- resp$long_run_cov
d <- resp$d