multiwave (version 1.4)

mfw_eval: evaluation of multivariate Fourier Whittle estimator

Description

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

Usage

mfw_eval(d, x, m)

Arguments

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.

Value

multivariate Fourier Whittle estimator computed at point d.

Details

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 \(N^{0.65}\).

References

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.

See Also

mfw_cov_eval, mfw

Examples

# NOT RUN {
### 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

# }