J. Japan Statist. Soc., Vol. 36 (No. 2), pp. 149-171, 2006

Inference on the Cointegration Rank and a Procedure for VARMA Root-Modification

Taro Takimoto and Yuzo Hosoya

Abstract. The paper presents a feasible numerical procedure for evaluating the maximum Whittle likelihood estimates and the likelihood-ratio statistics, where to obtain the maximum Whittle likelihood estimates under specific cointegration ranks, we introduce an iterative method in which the set of the ARMA coefficient estimates is adjusted so as to guarantee that in each step they satisfy the root conditions imposed by respective cointegration rank hypotheses. The method is incorporated in the Whittle likelihood maximization.

Key words and phrases: Cointegration rank test, invertibility, Jordan canonical form, stationarity, Whittle estimator.

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