Fisher information and equilibrium distributions in econophysics

Hawkins, Raymond J.; Frieden, B. Roy

doi:10.1016/j.physleta.2003.12.054

Cited by 26 publications

(26 citation statements)

References 11 publications

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“…The success of the approach in a wide range of amplitude-estimation problems [3], [4], [18]- [22], [23], [24], [25] implies that systems in general obey EP I through variation of their P DF s or amplitude f unctions. However, it is not known at this point whether systems as well obey EP I through variation of their channel f unctions.…”

Section: B Some Caveats To Epi Derivationmentioning

confidence: 99%

“…Second, only the right-hand term of (21) Result (25) shows that the attribute value a must be a multiple of 1/4, or, the powers in the power law (20) are multiples of 1/4. This is an important milestone in the biological derivation.…”

Section: B Primary Variation Of the System Function Leads To A Familmentioning

confidence: 99%

“…IV) to hold for the particular powers a n given by (25) that enforce a further extremization in the problem (2). Using powers (25) in the power law solution (42), and also using (5), gives…”

Section: E Final Allometric Lawsmentioning

confidence: 99%

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Power laws of complex systems from extreme physical information

Frieden

Gatenby

2005

Phys. Rev. E

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Many complex systems obey allometric, or power, laws y = Y x a . Here y ≥ 0 is the measured value of some system attribute a, Y ≥ 0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4, n = 0, ±1, ±2... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n = −1). Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I − J = extrem.of Extreme physical information (EPI) is found to provide such a cause. It describes the flow of Fisher information J → I from an attribute value a on the cell level to its exterior observation y. Data y are formed via a system channel function y ≡ f (x, a), with f (x, a) to be found. Extremizing the difference I − J through variation of f (x, a) results in a general allometric law f (x, a) ≡ y = Y x a . Darwinian evolution is presumed to cause a second extremization of I − J, now with respect to the choice of a. The solution is a = n/4, n = 0, ±1, ±2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by but two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients 1

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Section: B Some Caveats To Epi Derivationmentioning

confidence: 99%

Section: B Primary Variation Of the System Function Leads To A Familmentioning

confidence: 99%

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Power laws of complex systems from extreme physical information

Frieden

Gatenby

2005

Phys. Rev. E

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“…Our application of Fisher information to yield curve dynamics is an extension of prior work [1,2,3] using this approach to derive equations of motion in physics and static probability densities in asset pricing theory 2 . Though less well known as a measure of information in physics and mathematical finance than Shannon entropy, the concept of Fisher information predates Shannon's and other information statistics, and remains central to the field of statistical measurement theory [6].…”

mentioning

confidence: 99%

“…Our explanation for the existence of dynamic yield-curve modes builds on our recent application of Fisher information methods [2,3] to the construction of well-mannered, static yield curves from a finite set of discount functions or observed bond prices. Our approach, based on deriving yield curves that extremize Fisher information, is facilitated by associating such yield curves with complementary probability density functions where the time to maturity T is taken to be an abstract random variable [24,25].…”

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confidence: 99%

Ab initio yield curve dynamics

2005

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We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success of the Nelson Siegel approach to fitting static yield curves and the empirically observed modal structure of yield curves. A practical numerical implementation of this equation of motion is found by using the Karhunen-Lòeve expansion and Galerkin's method to formulate a reduced-order model of yield curve dynamics.Key words: Bond, interest rate, dynamics, Fisher information, yield curve, term structure, principal-component analysis, proper orthogonal decomposition, Karhunen-Lòeve, Galerkin, Fokker-Planck. PACS: 89.65. Gh, 89.70.+c Yield curves are remarkable in that the fluctuations of these structures can be explained largely by a few modes and that the shape of these modes is largely independent of the market of origin: a combination of parsimony and explanatory power rarely seen in financial economics. While these modes play a fundamental role in fixed-income analysis and risk management, both the origin of this modal structure and the relationship between this modal structure and a formal description of yield curve dynamics remain unclear. The purpose of this letter is to show that this modal structure is a natural consequence of the information structure of the yield curve and that this information structure, in turn, implies an equation of motion for yield curve dynamics.1 We thank Prof. Ewan Wright for helpful discussions and encouragement.

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Extreme Physical Information as a Principle of Universal Stability

Frieden

Information Theory and Statistical Learning

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Fisher information and equilibrium distributions in econophysics

Cited by 26 publications

References 11 publications

Power laws of complex systems from extreme physical information

Power laws of complex systems from extreme physical information

Ab initio yield curve dynamics

Extreme Physical Information as a Principle of Universal Stability

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