Canonical Momenta Indicators of Financial Markets and Neocortical EEG
Lester Ingber
Lester Ingber Research
P.O. Box 857, McLean, Virginia 22101, U.S.A.
[email protected], [email protected]
Abstract—A paradigm of statistical mechanics of financial markets (SMFM) is fit to multivariate financial
markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum
likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical
momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to
tune trading rules.
These trading rules are then used on outofsample data, to demonstrate that they can
profit from the SMFM model, to illustrate that these markets are likely not efficient.
This methodology can
be extended to other systems, e.g., electroencephalography. This approach to complex systems emphasizes the
utility of blending an intuitive and powerful mathematicalphysics formalism to generate indicators which are
used by AItype rulebased models of management.
1. Introduction
Over a decade ago, the author published a paper suggesting the use of newly developed methods of
multivariate nonlinear nonequilibrium calculus to approach a statistical mechanics of financial markets (SMFM) [1].
These methods were applied to interestrate termstructure systems [2,3]. Still, for some time, the standard accepted
paradigm of financial markets has been rooted in equilibrium processes [4]. There is a current effort by many to
examine nonlinear and nonequilibrium processes in these markets [5], and this paper reinforces this point of view.
Another paper gives some earlier 1991 results using this approach [6].
There are several issues that are clarified here, by presenting calculations of a specific trading model: (A) It is
demonstrated how multivariate markets might be formulated in a nonequilibrium paradigm.
(B) It is demonstrated
that numerical methods of global optimization can be used to fit such SMFM models to data.
(C) A variational
principle possessed by SMFM permits derivation of technical indicators, such as canonical momenta, that can be
used to describe deviations from most likely evolving states of the multivariate system.
(D) These technical
indicators can be embedded in realistic trading scenarios, to test whether they can profit from nonequilibrium in
markets.
Section 2 outlines the formalism used to develop the nonlinear nonequilibrium SMFM model.
Section 3
describes application of SMFM to SP500 cash and future data, using Adaptive Simulated Annealing (ASA) [7] to fit
the shorttime conditional probabilities developed in Section 2, and to establish trading rules by recursively
optimizing with ASA, using optimized technical indicators developed from SMFM.
These calculations were briefly
mentioned in another ASA paper [8]. Section 4 describes similar applications, now in progress, to correlating
customized electroencephalographic (EEG) momenta indicators to physiological and behavioral states of humans.
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 Winter '11
 BARNARD
 Physics, Thermodynamics, mechanics, pH, Statistical Mechanics, Entropy, The Land, Nonequilibrium thermodynamics

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