TY - GEN
A1 - Schroeder, Christian
A1 - Bruell, Tobias
A1 - Poloni, Federico
A1 - Sbrana, Giacomo
T1 - Enforcing solvability of a nonlinear matrix equation and estimation of multivariate ARMA time series
N2 - The matrix equation $X+AX^{-1}A^T=B$, arising in parameter estimation of certain time series models,
is solvable only for certain values of the matrices $A,B$.
We present a numerical method to modify $A,B$ in order to make the matrix equation solvable.
Since solvability depends on the location of the eigenvalues of the palindromic matrix polynomial $\lambda^2 A+\lambda B+A^T$,
our method works by moving those eigenvalues to specified locations using first order spectral perturbation theory.
The method is heuristic but works in practice, as is supported by several compelling numerical examples.
These examples arise from parameter estimation of a common time series model, the multivariate ARMA(1,1).
KW - regularization
KW - palindromic eigenvalue problem
KW - first order eigenvalue perturbation theory
KW - parameter estimation
KW - VARMA(1,1) model
Y1 - 2013
UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1240
UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12409
ER -