Maximum likelihood estimation in space time bilinear models

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.