fivarma {multiwave}

simulation of FIVARMA process

Description

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

Usage

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

Arguments

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).

Details

Let (e(t))_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.

Value

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.

Author(s)

S. Achard and I. Gannaz

References

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.

See Also

varma, vfracdiff

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