“Reverse Engineering” in Econophysics

“Reverse Engineering” in Econophysics

M.P. Hanias (Department of Electrical Engineering, Eastern Macedonia and Thrace Institute of Technology, Kavala, Greece), L. Magafas (Department of Electrical Engineering, Eastern Macedonia and Thrace Institute of Technology, Kavala, Greece) and S.G. Stavrinides (School of Science and Technology, International Hellenic University, Thermi-Thessaloniki, Greece)
DOI: 10.4018/IJPMAT.2019010103

Abstract

The work presented here is a paradigm of EconoPhysics, i.e. of research in the area of finance and economics by applying physical models, in this case chaos theory. A specific analysis of a macroeconomic model proposed by Vosvrda is presented. The Vosvrda model is an idealized macroeconomic model, combining the savings of households, Gross Domestic Product and the foreign capital inflow. It is simulated by three autonomous differential equations. According to this model, there are six parameters, having their values regulating the system behavior (parameters of Vosvdra). Using artificial noisy data for simulating real data and using an inverse modelling procedure, the authors have fitted and tuned the parameters of Vosvdra differential equations to achieve more accurate solutions. The relevant resultant evaluation showed that the system is a chaotic one, even though for the same values proposed by Vosvrda. Finally, this chaotic behavior has provided the capability to expand the time horizon of the solution, thus achieving reliable forecasting for the system.
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Methodology

The proposed hereby methodology for predicting specific characteristics of a system by utilizing past-time data, by exploiting nonlinear dynamics for expanding the time horizon, is briefly aposed (in the form of steps) in the lines that follow:

  • Step 1: Few real data for all the variables of the system is collected.

  • Step 2: The proper set of differential equations as this is “guessed” by theoretical considerations or by trial and error, is constructed.

  • Step 3: Initial values of all the parameters are set; some of them maybe partially known.

  • Step 4: The system’s set of differential equations is solved, and the solution is compared to the real data (validation process).

  • Step 5: The inverse modeling procedure is applied for all or some of the system’s parameters.

  • Step 6: The system’s set of differential equations is solved again with the new fitted parameter values (testing).

  • Step 7: Solving the set of differential equations is de facto expanding the time horizon, thus forecasting of the values of one or all of the variables is possible.

This methodology supposes that we have collected some real data for all variables of the specific system. But in case where we have collected one’s variable data only, then we must expand the methodology to include the other unknown data. In this case we can reconstruct the phase space according Taken’s theorem (Abarbanel, Brown, & Kadtke, 1990; Takens, 1980). From the reconstructed timeseries one can choose some points as real data. Then we can repeat the steps all over again.

It is apparent that this methodology is a kind of reverse engineering, exploiting at the same time the ability that deterministic chaotic systems have, to reconstruct the equivalent dynamics by one or more system variables.

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