Canonical Momenta Indicators of Financial Markets and Neocortical Eeg

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 out-of-sample 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 mathematical-physics formalism to generate indicators which are used by AI-type rule-based models of management.

[1]  B. LeBaron,et al.  Simple Technical Trading Rules and the Stochastic Properties of Stock Returns , 1992 .

[2]  Lester Ingber,et al.  Statistical mechanics of nonlinear nonequilibrium financial markets , 1984 .

[3]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  L. Ingber.  Statistical Mechanics of Neocortical Interactions. I. Basic Formulation , 2001 .

[5]  Michael F. Wehner,et al.  Mathematical comparison of combat computer models to exercise data , 1991 .

[6]  L. Ingber.  Statistical mechanics of multiple scales of neocortical interactions , 1995 .

[7]  Ingber,et al.  Statistical mechanics of neocortical interactions: Stability and duration of the 7+/-2 rule of short-term-memory capacity. , 1985, Physical review. A, General physics.

[8]  B. Mandelbrot.  When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models , 1971 .

[9]  Kuo‐shung Cheng,et al.  Quantization of a General Dynamical System by Feynman's Path Integration Formulation , 1972 .

[10]  R. Graham,et al.  Path-integral methods in Nonequilibrium Thermodynamics and statistics , 1978 .

[11]  L Ingber,et al.  Statistical mechanics of neocortical interactions: multiple scales of EEG. , 1996, Electroencephalography and clinical neurophysiology. Supplement.

[12]  P. Clark.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[13]  Ingber,et al.  Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[14]  L. Ingber.  Adaptive Simulated Annealing (ASA) , 1993 .

[15]  H. Haken,et al.  Synergetics , 1988, IEEE Circuits and Devices Magazine.

[16]  Ingber,et al.  Statistical mechanics of neocortical interactions: High-resolution path-integral calculation of short-term memory. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Ingber,et al.  Riemannian contributions to the short-ranged velocity-dependent nucleon-nucleon interaction. , 1986, Physical review. D, Particles and fields.

[18]  E. Tirapegui,et al.  SHORT DERIVATION OF FEYNMAN LAGRANGIAN FOR GENERAL DIFFUSION PROCESSES , 1980 .

[19]  L. Ingber.  Very fast simulated re-annealing , 1989 .

[20]  L. Ingber.  Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity , 1984 .

[21]  Lester Ingber,et al.  Path-integral Riemannian contributions to nuclear Schrödinger equation , 1984 .

[22]  Lester Ingber,et al.  Statistical mechanics of neocortical interactions. Dynamics of synaptic modification , 1983 .

[23]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[24]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[25]  Stephen L Taylor,et al.  Tests of the Random Walk Hypothesis Against a Price-Trend Hypothesis , 1982, Journal of Financial and Quantitative Analysis.

[26]  Ingber,et al.  Statistical-mechanical aids to calculating term-structure models. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[27]  M. C. Jensen.  Some Anomalous Evidence Regarding Market Efficiency , 1978 .

[28]  L. Ingber,et al.  Application of statistical mechanics methodology to term-structure bond-pricing models , 1991 .

[29]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .

[30]  Benoit B. Mandelbrot,et al.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices: Comment , 1973 .

[31]  Lester Ingber,et al.  Mesoscales in neocortex and in command, control and communications (C3) systems , 1988 .

[32]  Lester Ingber.  Mathematical comparison of JANUS(T) simulation to National Training Center , 1989 .

[33]  Lester Ingber.  Riemannian corrections to velocity-dependent nuclear forces , 1983 .

[34]  Lester Ingber,et al.  Statistical Mechanics of Nonlinear Nonequilibrium Financial Markets: Applications to Optimized Trading , 1996 .

[35]  Paul L. Nunez,et al.  Multiple scales of statistical physics of the neocortex: Application to electroencephalography , 1990 .

[36]  Ingber,et al.  Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  D. Sworder,et al.  Statistical mechanics of combat with human factors , 1991 .

[38]  Ingber,et al.  Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[39]  Lester Ingber,et al.  Statistical Mechanics of Neocortical Interactions: EEG Dispersion Relations , 1985, IEEE Transactions on Biomedical Engineering.

[40]  Carl Jones.  Statistical Mechanics of Combat and Extensions , 1993 .

[41]  E. Tirapegui,et al.  Discretization Problems of Functional Integrals in Phase Space , 1979 .