Estimates the non-diagonal autoregressive coefficient matrix \(\Phi\) and innovation covariance matrix \(\Sigma_{\boldsymbol{\nu}}\) for the residual process obtained after removing the estimated fluctuating mean from the data. The estimation applies the Lasso to encourage sparsity in the cross-variable dependence structure.
estimatePhinu_nondiag(
epsilons,
Sig_nu_diag,
Phi_diag,
replace_diag = FALSE,
needReproduce = FALSE
)A list containing:
`Phi_hat` — Estimated non-diagonal autoregressive matrix \(\Phi\).
`Sig_nu_hat` — Estimated non-diagonal innovation covariance matrix \(\Sigma_{\boldsymbol{\nu}}\).
Numeric matrix of dimension \(n \times p\), representing the estimated residuals \(\boldsymbol{\epsilon}_t = \mathbf{y}_t - \hat{\boldsymbol{\mu}}_t\).
Numeric \(p \times p\) diagonal matrix providing initial (diagonal) estimates of \(\Sigma_{\boldsymbol{\nu}}\).
Numeric \(p \times p\) diagonal matrix providing initial (diagonal) estimates of \(\Phi\).
Logical; if TRUE, replaces the diagonal
entries of the estimated matrices with those from
Sig_nu_diag and Phi_diag (default FALSE).
Logical; if TRUE, uses fixed fold assignments
in cross-validation to ensure reproducibility (default FALSE).
The function applies a Lasso-penalized VAR(1) fit to the residual
process \(\boldsymbol{\epsilon}_t\) to estimate cross-dependencies
among variables.
The fitting is performed using the function
fitVAR(), which is adapted from the sparsevar package.
When replace_diag = TRUE, the diagonal entries of
\(\Phi\) and \(\Sigma_{\boldsymbol{\nu}}\) are replaced by
their componentwise estimates obtained in Phase I for improved
numerical stability.