fivarma function

simulation of FIVARMA process

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

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

and

where L is the lag-operator.

Returns

• 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.

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.

Author(s)

S. Achard and I. Gannaz

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