Use of canonical analysis in time series model identification

Abstract

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.