In this paper we propose a class of space±time bilinear (STBL) models which can be used to model space±time series which exhibit bilinear behavior. The STBL model is shown to be an extension of a space±time autoregressive movingaverage model and a special form of the multiple bilinear model. We focus on the identi®cation procedure of the models. Some results about stationarity and the covariance structure of these models are also discussed. An identi®cation procedure based on the squared observations is established for the simplest pure bilinear model and some illustrative examples are provided.

The space time bilinear (STBL) model is a special form of a multiple bilinear time series that can be used to model time series which exhibit bilinear behaviour on a spatial neighbourhood structure. The STBL model and its identification have been proposed and discussed by Dai and Billard (1998). The present work considers the problem of parameter estimation for the STBL model. A conditional maximum likelihood estimation procedure is provided through the use of a Newton-Raphson numerical optimization algorithm. The gradient vector and Hessian matrix are derived together with recursive equations for computation implementation. The methodology is illustrated with two simulated data sets, and one real-life data set.