Statistical Validation of Multi-Agent Financial Models Using the H-Infinity Kalman Filter

The article develops a method that is based on the H-infinity Kalman Filter for statistical validation of models of multi-agent financial systems in the form of an oligopoly. The real outputs of the oligopoly are compared against the outputs of an H-infinity Kalman Filter estimator that incorporates the oligopoly’s dynamic model. The difference between the two outputs forms the residuals’ sequence. The residuals undergo statistical processing. Actually, the sum of the products between the residual vectors’ square and the inverse of their covariance matrix defines a stochastic variable which follows the $$\chi ^2$$ χ 2 distribution and which provides a statistical test about the existence or absence of parametric changes in the oligopolistic market. Next, by exploiting the properties of the $$\chi ^2$$ χ 2 distribution one can define confidence intervals to validate the model used by the H-infinity Kalman Filter, in comparison to the real dynamics of the oligopoly. By validating the models that describe the dynamics of multi-agent financial systems one can perform reliable forecasting, and more efficient decision making or risk management.