On The Existence Of A General Multiple Bilinear Time Series

. A sufficient condition is derived for the existence of a strictly stationary solution of the general multiple bilinear time series equations (without assuming subdiagonality). The condition is shown to reduce to the condition of Stensholt and Tjostheim in the special case which they consider. Under this condition a solution is constructed which is shown to be casual in the sense we define, strictly stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non‐linear terms, i.e. the multiple autoregressive moving‐average (ARMA) model. the condition given here reduces to the well‐known sufficient condition for the existence of a casual stationary solution.