Model Validation in Non-Linear Continuous-Discrete Grey-Box Models

The validation part of the modeling procedure is used in the iterative process of model building and as an acceptance test of the obtained model. This paper presents a number of tools for validating non-linear continuous-discrete time stochastic state space models. For equidistantly sampled data a minor transformation of the one-step prediction errors is appropriate and the tools applied can also be used to suggest extensions of the model. Alternatively, we may regard the diffusion term as unmodelled systematic variation and in this case use the estimated diffusion as a tool to suggest possible sources of such variation. Finally, in the general case we may apply a transformation, based on numerical solution of the Fokker-Planck equation, in order to obtain standardized residuals which under the model are i.i.d. Gaussian. Standard tests can then be applied to these residuals.