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Biometrika 1985 72(2):299-315; doi:10.1093/biomet/72.2.299
© 1985 by Biometrika Trust
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Use of canonical analysis in time series model identification

RUEY S. TSAY and GEORGE C. TIAO

Department of Statistics, Carnegie-Mellon University Pittsburgh, Pennsylvania 15213, U.S.A
Graduate School of Business, University of Chicago Chicago, Illinois 60637, U.S.A

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 autoregressive-moving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the auto-regressive parameters involved. The asymptotic distribution of the identification statistic is discussed.

Key Words: Autoregressive moving average model • Canonical correlation • Extended sample autocorrelation • Least squares • Time series


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