Nonlinear statistical models
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A method has been developed to estimate the parameters of systems of nonlinear stochastic differential equations. This method uses quasilinearization at each observation and conditional least squares for the loss function on the one step ahead prediction. This method has been applied to estimate the parameters of a S-system that models the feeding and growth of animals. This application has been programmed in the GAUSS language for IBM/PC microcomputers. A related simulation program has also been programmed in GAUSS and has been used to evaluate the distribution of parameter estimates for a two equation three parameter S-system. Theoretical results for conditional least squares imply assymptopic normality of these parameter estimates. The simulation results for 30 time periods indicate that some parameter estimates approach normality in relatively small samples while others require longer series. The algorithm allows the inclusion of unobserved variables in the S-system. The result is to allow for the possibility of an ARMA error process in the observed variables. The complete listing of the code is available upon request to the author.