On the identifiability of bilinear stochastic systems

Bilinear systems are useful to model nonlinear time series. They can be described by a nonlinear recursive equation involving a finite number of parameters. Their analysis and particularly the estimation of the parameters is of central interest. In this paper we establish difference equations between lagged moments and cumulants up to third-order of a simple bilinear model, and show how to use these relations to estimate the parameters