weakARMA (version 1.0.3)

matXi: Estimation of Fisher information matrix I

Description

Uses a consistent estimator of the matrix I based on an autoregressive spectral estimator.

Usage

matXi(data, p = 0, q = 0)

Arguments

data

Matrix of dimension (p+q,n).

p

Dimension of AR estimate coefficients.

q

Dimension of MA estimate coefficients.

Value

Estimate Fisher information matrix \(I = \sum_{h=-\infty}^{+\infty} cov(2e_t \nabla e_t, 2e_{t-h} \nabla e_{t-h})\) where \(\nabla e_t\) denotes the gradient of the residuals.

References

Berk, Kenneth N. 1974, Consistent autoregressive spectral estimates, The Annals of Statistics, vol. 2, pp. 489-502.

Boubacar Ma<U+00EF>nassara, Y. and Francq, C. 2011, Estimating structural VARMA models with uncorrelated but non-independent error terms, Journal of Multivariate Analysis, vol. 102, no. 3, pp. 496-505.

Boubacar Mainassara, Y. and Carbon, M. and Francq, C. 2012, Computing and estimating information matrices of weak ARMA models Computational Statistics & Data Analysis, vol. 56, no. 2, pp. 345-361.