mfw function

multivariate Fourier Whittle estimators

Computes the multivariate Fourier Whittle estimators of the long-memory parameters and the long-run covariance matrix also called fractal connectivity.

mfw(x, m)

Arguments

• 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 $N^0.65$.

Returns

• d: estimation of the vector of long-memory parameters.

• cov: estimation of the long-run covariance matrix.

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.

Author(s)

S. Achard and I. Gannaz

See Also

mfw_eval, mfw_cov_eval

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 2007
res_mfw <- mfw(x,m)