A Multicriteria Method for Identification and Forecasting

Abstract

A multicriteria approach to identify and forecast mathematical models is considered. The need for such an approach arises, in particular, when it is necessary to take into account errors that cannot be reduced to one function and in the absence of specific information about the data interference class. The paper deals with a multicriteria version of the identification sets method based on approximating and visualizing the graph of the vector function of identification errors and its projections onto the space of identification parameters. The nearness function is introduced that describes the proximity of a criterion point to the set of nonimprovable (Pareto efficient) solutions of the identification problem. The efficient criteria set (Pareto frontier), the sets of efficient and subefficient parameters, and the corresponding forecast trajectory tubes are studied. To construct these objects, methods for approximating implicitly specified sets are used, in particular, methods for approximating the Edgeworth–Pareto hull and the deep holes method. The technique and examples for two criteria of identification quality are considered in detail.