What Economists can learn from physics and finance

Some economists (Mirowski, 2002) have asserted that the neoclassical economic model was motivated by Newtonian mechanics. This viewpoint encourages confusion. Theoretical mechanics is firmly grounded in reproducible empirical observations and experiments, and provides a very accurate description of macroscopic motions to within high decimal precision. In stark contrast, neo-classical economics, or ‘rational expectations’ (ratex), is a merely postulated model that cannot be used to describe any real market or economy, even to zeroth order in perturbation theory. In mechanics we study both chaotic and complex dynamics whereas ratex restricts itself to equilibrium. Wigner (1967) has isolated the reasons for what he called ‘the unreasonable effectiveness of mathematics in physics’. In this article we isolate the reason for what Velupillai (2005), who was motivated by Wigner (1960), has called the ineffectiveness of mathematics in economics. I propose a remedy, namely, that economic theory should strive for the same degree of empirical success in modeling markets and economies as is exhibited by finance theory.Nonequilibrium; empirically based modelling; stochastic processes; complexity

An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is selected to capture the slow, macroscopic behavior of the system, and the family of quasi-equilibrium probability densities on phase space corresponding to these resolved variables is employed as a statistical model. The macroscopic dynamics of the mean resolved variables is determined by optimizing over paths of these probability densities. Specifically, a cost function is introduced that quantifies the lack-of-fit of such paths to the underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of the residual that results from submitting a path of trial densities to the Liouville equation. The evolution of the macrostate is estimated by minimizing the time integral of the cost function. The value function for this optimization satisfies the associated Hamilton-Jacobi equation, and it determines the optimal relation between the statistical parameters and the irreversible fluxes of the resolved variables, thereby closing the reduced dynamics. The resulting equations for the macroscopic variables have the generic form of governing equations for nonequilibrium thermodynamics, and they furnish a rational extension of the classical equations of linear irreversible thermodynamics beyond the near-equilibrium regime. In particular, the value function is a thermodynamic potential that extends the classical dissipation function and supplies the nonlinear relation between thermodynamics forces and fluxes

Making dynamic modelling effective in economics

Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are nonstationary. This means that 'value' is subjective. Nonstationarity also means that the form of the noise in a market cannot be postulated a priroi, but must be deduced from the empirical data. I discuss the essence of complexity in a market as unexpected events, and end with a biological speculation about market growth.Economics; fniancial markets; stochastic process; Markov process; complex systems

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolut ion. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.Comment: LaTeX 2e (elsart), 17 pages, 3 EPS figures and 2 tables, accepted for publication in Physica

Forecasting critical transitions using data-driven nonstationary dynamical modeling

This is the final version of the article. Available from American Physical Society via the DOI in this record.An approach to predicting critical transitions from time series is introduced. A nonstationary low-order stochastic dynamical model of appropriate complexity to capture the transition mechanism under consideration is estimated from data. In the simplest case, the model is a one-dimensional effective Langevin equation, but also higher-dimensional dynamical reconstructions based on time-delay embedding and local modeling are considered. Integrations with the nonstationary models are performed beyond the learning data window to predict the nature and timing of critical transitions. The technique is generic, not requiring detailed a priori knowledge about the underlying dynamics of the system. The method is demonstrated to successfully predict a fold and a Hopf bifurcation well beyond the learning data window

Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate