mfw_eval: evaluation of multivariate Fourier Whittle estimator
In multiwave: Estimation of Multivariate Long-Memory Models Parameters

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

Evaluates the multivariate Fourier Whittle criterion at a given long-memory parameter value d.

1	mfw_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.

multivariate Fourier Whittle estimator computed at point d.

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_cov_eval, mfw

### Simulation of ARFIMA(0,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
res_mfw <- mfw(x,m)
d <- res_mfw$d
G <- mfw_eval(d,x,m)
k <- length(d)
res_d <- optim(rep(0,k),mfw_eval,x=x,m=m,method='Nelder-Mead',lower=-Inf,upper=Inf)$par