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 -