A Decision Procedure for Bilinear Time Series Based on the Asymptotic Separation

Abstract

This paper presents a non-classical decision procedure for a bilinear model with a general error process. This procedure allows us to decide, in a consistent way, between two hypotheses on the model. By establishing the asymptotic separation of the sequences of probability laws defined by each hypothesis, we obtain the consistence of this decision method. Some studies about the rate of convergence are presented and an exponential decay is obtained. A simulation study is done to illustrate the behaviour of the power and level functions in small and moderate samples when this procedure is used as a test.

AMS Classification::

• 62M10

Keywords:

• Time Series
• asymptotic separation
• bilinear models
• test