In the present article, we are interested in the identification of canonical ARMA echelon form models represented in a "refined" form. An identification procedure for such models is given by Tsay (J. Time Ser. Anal.10(1989), 357-372). This procedure is based on the theory of canonical analysis. We propose an alternative procedure which does not rely on this theory. We show initially that an examination of the linear dependency structure of the rows of the Hankel matrix of correlations, with originkin (i.e., with correlation at lagkin position (1, 1)), allows us not only to identify the Kronecker indicesn1, ..., nd, whenk=1, but also to determine the autoregressive ordersp1, ..., pd, as well as the moving average ordersq1, ..., qdof the ARMA echelon form model by settingk>1 andk<1, respectively. Successive test procedures for the identification of the structural parametersni,pi, andqiare then presented. We show, under the corresponding null hypotheses, that the test statistics employed asymptotically follow chi-square distributions. Furthermore, under the alternative hypothesis, these statistics are unbounded in probability and are of the formN[delta]{1+op(1)}, where[delta]is a positive constant andNdenotes the number of observations. Finally, the behaviour of the proposed identification procedure is illustrated with a simulated series from a given ARMA model.
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Volume (Year): 56 (1996) Issue (Month): 2 (February) Pages: 207-231 Download reference. The following formats are available: HTML
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