The eigenvalues of an unknown linear dynamical system's state-transition matrix can be consistently estimated from output time series by fitting the autoregressive parameters of an ARMA model, at a root-T convergence rate.
TheO(ϵ) convergence rate then follows from Lemma B.2 and Theorem 5.1, as the error on ARMAX parameter estimation can be seen as perturbation on the companion matrix
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Linear Dynamics: Clustering without identification
The eigenvalues of an unknown linear dynamical system's state-transition matrix can be consistently estimated from output time series by fitting the autoregressive parameters of an ARMA model, at a root-T convergence rate.