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See detailFinancial interaction networks inferred from traded volumes
Zeng, Hong-Li; Lemoy, Rémi UL; Alava, Mikko

in Journal of Statistical Mechanics: Theory and Experiment (2014)

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation ... [more ▼]

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed. [less ▲]

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See detailGenerally covariant state-dependent diffusion
Polettini, Matteo UL

in Journal of Statistical Mechanics: Theory and Experiment (2013), (07),

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non-gauge-invariant ... [more ▼]

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non-gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of external forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless incorporates the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The overdamping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Itō, Stratonovich or other). At odds with the latter interpretations, the corresponding Fokker–Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the nonuniform steady spatial distribution. [less ▲]

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