Linear stochastic systems
The statistical theory of linear systems
The statistical theory of linear systems
Identification and stochastic adaptive control
Identification and stochastic adaptive control
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Brief paper: Recursive identification for multivariate errors-in-variables systems
Automatica (Journal of IFAC)
Robust and accurate ARX and ARMA model order estimation ofnon-Gaussian processes
IEEE Transactions on Signal Processing
MA estimation in polynomial time
IEEE Transactions on Signal Processing
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Let the observation $\{y_k\}$ be generated by the multivariate ARMA process $A(z)y_k=C(z)w_k$ with unknown coefficients $\theta_A$, $\theta_C$ and orders $(p,r)$, where $\{w_k\}$ is a sequence of independent and identically distributed (i.i.d.) random vectors with zero mean and unknown covariance matrix $R_w0$. A new method for estimating the orders $(p,r)$ is introduced. In contrast to most of the existing results, the new method is not based on optimizing a certain criterion, and the order estimates given in the paper are rather easy to update computationally in comparison with the criterion-optimization-based methods when new data arrive. The method is then extended to determining the orders of ARMAX processes. Under reasonable conditions the estimates are proved to converge to the true orders with probability one as time tends to infinity.