DIFFERENCE EQUATIONS FOR HIGHER-ORDER MOMENTS AND CUMULANTS FOR THE BILINEAR TIME SERIES MODEL BL(p, 0, p, 1)

Abstract. In this paper we obtain difference equations for higher-order moments and cumulants for the time series { X _t} satisfying the bilinear model BL( p , 0, p , 1). These equations are similar to the well-known Yule-Walker equations for the autoregressive moving-average model which are in terms of the second-order covariances. Thus they can be used for the tentative identification of bilinear models. Another application of these equations is in the computation of preliminary estimates of the parameters of the model. We shall illustrate this by means of simulations for two simple examples of bilinear models.