Statistical Validation of Multi-Agent Financial Models Using the H-Infinity Kalman Filter
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Statistical Validation of Multi‑Agent Financial Models Using the H‑Infinity Kalman Filter G. Rigatos1 Accepted: 11 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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 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 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. Keywords Multi-agent financial models · Oligopolies · Model validation · Statistical change detection · Change threshold · 𝜒 2 distribution · H-infinity Kalman Filter
1 Introduction Multi-agent models appear in several forms of economic activity, for instance in oligopolies that trade electric power, oil, natural gas, mining products and other highvalue commodities (Rigatos 2017; Rigatos et al. 2019; Day et al. 2002; Punchuk and Puu 2010; Elettreby and Hassan 2006; Yang et al. 2015; Tramontana and Elsaduny 2012; Puu and Norin 2003). Modelling of multi-agent financial systems is critical for understanding how the state of the individual agents evolves in-time, and which are the interactions and couplings between such agents, as well as their responsiveness * G. Rigatos [email protected] 1
Unit of Industrial Automation, Industrial Systems Institute, 26504 Rion Patras, Greece
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to exogenous inputs (Andaluz et al. 2017; Ding et al. 2014; Richter and Stalk 2004; Agliari et al. 2000). To this end, several models have been developed in an aim to describe how firms modify their production rate within an oligopoly and how the individual levels of production get stabilized at local equilibria (Ahmed and Elettreby 2014; Asker 2007; Cerboni Baiardi and Naimzada 2017; Tramontana et al. 2015). Such models can explain how the price of the oligopolies’ products occasionally reaches a steady value. It is important to model precisely, the dynamics of multi-agent financial systems and particularly of oligopolies since such models are used in forecasting and in several forms of decision making (Hong et al. 2014; Farni et al. 2016; Komunjer and Zhu 2015; Wilcox and Hamano 2017; L
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