Cumulant-Based Order Determination of Non-Gaussian ARMA Models

Georgios B. Giannakis, Jerry M. Mendel

Research output: Contribution to journalArticlepeer-review

145 Scopus citations


Higher than second-order cumulants can be used for order determination of non-Gaussian ARMA processes. The two methods developed assume knowledge of upper bounds on the ARMA orders. The first method performs a linear dependency search among the columns of a higher order statistics matrix, via the Gram-Schmidt ortho-gonalization procedure. In the second method, the order of the AR part is found as the rank of the matrix formed by the higher order statistics sequence. For numerically robust rank determination the singular value decomposition approach is adopted. Furthermore, using the argument principle and samples of the polyspectral phase the relative degree of the ARMA model is obtained from which the order of the MA part can be determined. Statistical analysis is included for determining the correct MA order with high probability, when estimates of third-order cumulants are only available. Simulations verify the performance of our methods, and compare autocorrelation with cu-mulant-based order determination approaches.

Original languageEnglish (US)
Pages (from-to)1411-1423
Number of pages13
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Issue number8
StatePublished - Aug 1990

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