Abstract In recent years there has been a growing interest in

studying bilinear time series models. However, there are difficult problems

related to the order identification of these models. In this paper, we

consider the bilinear time series models, Xt = BXt-k et-1 + et , k>i, k=i

and k<i, and propose some methods of order identification based on the

structure of autocovarance of {X2t} and the third-order-automoment of

{xt}. Decision rules as well as simulated bilinear time series are

compared. An advantage of our methods is its simple of implementation.

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