Use of canonical analysis in time series model identification

SUMMARY The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressivemoving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the autoregressive parameters involved. The asymptotic distribution of the identification statistic is discussed.

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