mfw_cov_eval: multivariate Fourier Whittle estimators
In multiwave: Estimation of Multivariate Long-Memory Models Parameters

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

Computes the multivariate Fourier Whittle estimator of the long-run covariance matrix (also called fractal connectivity) for a given value of long-memory parameters d.

1	mfw_cov_eval(d, x, m)

`d`	vector of long-memory parameters (dimension should match dimension of x)
`x`	data (matrix with time in rows and variables in columns)
`m`	truncation number used for the estimation of the periodogram

The choice of m determines the range of frequencies used in the computation of the periodogram, lambda_j = 2*pi*j/N, j = 1,... , m. The optimal value depends on the spectral properties of the time series such as the presence of short range dependence. In Shimotsu (2007), m is chosen to be equal to N^0.65.

long-run covariance matrix estimation.

S. Achard and I. Gannaz

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

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.

mfw_eval, mfw

### Simulation of ARFIMA(0,\code{d},0)
rho <- 0.4
cov <- matrix(c(1,rho,rho,1),2,2)
d <- c(0.4,0.2)
J <- 9
N <- 2^J

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

m <- 57 ## default value of Shimotsu
G <- mfw_cov_eval(d,x,m) # estimation of the covariance matrix when d is known