Asymptotic Separation in Bilinear Models

E. Gonçalves, C.M. Martins and N. Mendes-Lopes

Abstract: This paper presents a generalization of a non-classical decision procedure for simple bilinear models with a general error process, proposed by Gonçalves, Jacob and Mendes-Lopes [11]. This decision method involves two hypotheses on the model and its consistence is obtained by establishing the asymptotic separation of the sequences of probability laws defined by each hypothesis. Studies on the rate of convergence in the diagonal case are presented and an exponential decay is obtained. Simulation experiments are used to illustrate the behaviour of the power and level functions in small and moderate samples when this procedure is used as a test.

Keywords: Time series; asymptotic separation; bilinear models; test.

Classification (MSC2000): 62M10, 62F03.

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