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.
Hence the outputsyt are generated by an ARMA(n,n) process as claimed in Theorem 4.1
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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.