mfw_eval {multiwave}

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.

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}.

Value

multivariate Fourier Whittle estimator computed at point d.

Author(s)

S. Achard and I. Gannaz

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

### 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