Inferring Microscopic Financial Information from the Long Memory in Market-Order Flow: A Quantitative Test of the Lillo-Mike-Farmer Model.

In financial markets, the market-order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign autocorrelation function (ACF) displays long memory with power-law exponent γ, such that C(τ)∝τ^{-γ} for large time-lag τ. One of the most promising microscopic hypotheses is the order-splitting behavior at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behavior, which predicts that the macroscopic sign correlation is quantitatively associated with the microscopic distribution of metaorders. While this hypothesis has been a central issue of debate in econophysics, its direct quantitative validation has been missing because it requires large microscopic datasets with high resolution to observe the order-splitting behavior of all individual traders. Here we present the first quantitative validation of this LMF prediction by analyzing a large microscopic dataset in the Tokyo Stock Exchange market for more than nine years. On classifying all traders as either order-splitting traders or random traders as a statistical clustering, we directly measured the metaorder-length distributions P(L)∝L^{-α-1} as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation γ≈α-1. We discover that the LMF prediction agrees with the actual data even at the quantitative level. We also discuss the estimation of the total number of the order-splitting traders from the ACF prefactor, showing that microscopic financial information can be inferred from the LRC in the ACF. Our Letter provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure.

Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes.

The origin(s) of the ubiquity of probability distribution functions with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences. In parallel, self-excited dynamics is a prevalent characteristic of many systems, from the physics of shot noise and intermittent processes, to seismicity, financial and social systems. Motivated by activation processes of the Arrhenius form, we bring the two threads together by introducing a general class of nonlinear self-excited point processes with fast-accelerating intensities as a function of "tension." Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the probability distribution functions of their intensities described by a power law on the condition that (i) the intensity is a fast-accelerating function of tension, (ii) the distribution of marks is two sided with nonpositive mean, and (iii) it has fast-decaying tails. In particular, Zipf's scaling is obtained in the limit where the average mark is vanishing. This unearths a novel mechanism for power laws including Zipf's law, providing a new understanding of their ubiquity.

Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach.

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological, and economic systems. By expressing the probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function of the intensities close to the critical point n=1 of the Hawkes process, with a nonuniversal exponent, function of the background intensity ν_{0} of the Hawkes intensity, the average timescale of the memory kernel and the branching ratio n. Our theoretical predictions are confirmed by numerical simulations.

Loopy Lévy flights enhance tracer diffusion in active suspensions.

Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3-10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15.

Ecology of trading strategies in a forex market for limit and market orders.

There is a growing interest to understand financial markets as ecological systems, where the variety of trading strategies correspond to that of biological species. For this purpose, transaction data for individual traders are studied recently as empirical analyses. However, there are few empirical studies addressing how traders submit limit and market order at the level of individual traders. Since limit and market orders are key ingredients finally leading to transactions, it would be necessary to understand what kind of strategies are actually employed among traders before making transactions. Here we demonstrate the variety of limit-order and market-order strategies and show their roles in the financial markets from an ecological perspective. We find these trading strategies can be well-characterized by their response pattern to historical price changes. By applying a clustering analysis, we provide an overall picture of trading strategies as an ecological matrix, illustrating that liquidity consumers are likely to exhibit high trading performances compared with liquidity providers. Furthermore, we reveal both high-frequency traders (HFTs) and low-frequency traders (LFTs) exhibit high trading performance, despite the difference in their trading styles; HFTs attempt to maximize their trading efficiency by reducing risk, whereas LFTs make their profit by taking risk.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders.

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Granular rotor as a probe for a nonequilibrium bath.

This study numerically and analytically investigates the dynamics of a rotor under viscous or dry friction as a nonequilibrium probe of a granular gas. In order to demonstrate the role of the rotor as a probe for a nonequilibrium bath, the molecular dynamics (MD) simulation of the rotor is performed under viscous or dry friction surrounded by a steady granular gas under gravity. A one-to-one map between the velocity distribution function (VDF) of the granular gas and the angular distribution function for the rotor is theoretically derived. The MD simulation demonstrates that the one-to-one map accurately infers the local VDF of the granular gas from the angular VDF of the rotor, and vice versa.

Minimal model of stochastic athermal systems: origin of non-Gaussian noise.

For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.

Energy pumping in electrical circuits under avalanche noise.

We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasistatic and finite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.

Heat conduction induced by non-Gaussian athermal fluctuations.

We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average and fluctuation are determined not only by the noise intensities but also by the non-Gaussian nature of the noises. Our results explicitly show the absence of the zeroth law of thermodynamics in athermal systems.

Stochastic energetics for non-Gaussian processes.

By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total energy difference into the work and the heat for each trajectory, and derive a formula to calculate the heat from experimental data on the dynamics. We apply our formulation and results to a Langevin system driven by a Poisson noise.

Self-assembled RANK induces osteoclastogenesis ligand-independently.

UNLABELLED: By immunoprecipitation assay, we showed that mouse RANK was self-assembled through its cytoplasmic domain located at position 534-539, whose domain was different form TRAF binding domains. Moreover, overexpression experiments showed that oligomeric RANK, which was self-associated, induced osteoclastogenesis ligand-independently. INTRODUCTION: TNF receptor I or II (TNF-RI or TNF-RII) is thought to induce its own trimerization by ligand binding; however, recently TNF-RI or TNF-RII was shown to form a trimer through its extracellular domain without ligand binding. RANK, which plays an important role in osteoclast differentiation, is a member of the TNF receptor family. Here, we studied the self-assembly of mouse RANK. MATERIALS AND METHODS: Self-assembly of mouse RANK was examined by immunoprecipitation assay using 293T cells that had been transfected with the full-length RANK (Full) fused to FLAG tag (Full-FLAG) and Full fused to HA tag (Full-HA) without soluble RANKL (sRANKL). To explore the binding site for self-assembly, FLAG-tagged RANK C-terminal deletion mutants, 461-, 511-, 533-, 539-, and 544-FLAG, were constructed, and immunoprecipitation was performed. To examine whether RANK overexpression induced osteoclastogenesis, osteoclast progenitors that were derived from wildtype bone marrow cells, in which RANK was overexpressed, were cultured with monocyte-macrophage colony-stimulating factor (M-CSF), and TRACP staining was performed. We examined whether overexpression of each five individual C-terminal mutants induced osteoclastogenesis in osteoclast progenitors. To study the involvement of TRAF6 in RANK-induced osteoclastogenesis, osteoclast progenitors, in which RANK was overexpressed, were cultured with M-CSF and TNF receptor-associated factor (TRAF)6 decoy peptides (T6DP) that inhibit the interaction of RANK with TRAF6. RESULTS AND CONCLUSIONS: Immunoprecipitation experiments showed that RANK was self-assembled without sRANKL. Among the five individual mutants, only 539- and 544-FLAG mutants were associated with Full-HA ligand-independently, suggesting that self-association of RANK was regulated by its cytoplasmic domain located at position 534-539. Overexpression of full-length RANK induced osteoclast differentiation, and this differentiation was suppressed by treatment with T6DP. Overexpression of RANK deletion mutants revealed that only 539- and 544-FLAG induced osteoclastogenesis. The five C-terminal mutants had the TRAF6 binding domain in their cytoplasmic regions, suggesting that ligand-independent osteoclastogenesis requires the receptor oligomerization of RANK.

TRAF2 is essential for TNF-alpha-induced osteoclastogenesis.

UNLABELLED: TRAF2-deficient mice show embryonic lethality, and we developed a new in vitro differentiation system to show the function of TRAF2 in osteoclastogenesis, in which osteoclast progenitors are derived from the fetal liver of TRAF2-deficient mice. Using this system, we showed that TRAF2 is required for TNF-alpha-induced osteoclastogenesis. INTRODUCTION: TNF receptor-associated factor 2 (TRAF2) is a signal transducer for RANK and for two TNF receptor isotypes, TNFR1 and TNFR2. Because TRAF2-deficient mice show embryonic lethality, it has remained unclear whether TRAF2 is crucial in RANKL- or TNF-alpha-induced osteoclastogenesis. MATERIALS AND METHODS: Osteoclast progenitors derived from fetal liver were cultured in the presence of monocyte macrophage colony-stimulating factor (M-CSF), and flow cytometry for characterization of surface markers on these cells was performed. To examine the involvement of TRAF2 in osteoclast differentiation, we cultured osteoclast progenitors from TRAF2-deficient and wildtype mice with soluble RANKL or TNF-alpha in the presence of M-CSF, and counted the number of TRACP(+) multinucleate cells formed. c-jun N-terminal kinase (JNK) and NF-kappaB activation in osteoclast progenitors was examined by Western blot analysis and electrophoretic mobility shift assay, respectively. Nuclear factor of activated T cells (NFATc1) expression and activation were analyzed by RT-PCR and immunofluorescence staining, respectively. To examine whether TRAF2 overexpression induced osteoclastogenesis, TRAF2 was overexpressed in osteoclast progenitors form wildtype bone marrow by retrovirus infection. RESULTS AND CONCLUSIONS: Osteoclast progenitors from normal fetal liver, which were cultured with M-CSF, expressed surface molecules c-fms, Mac-1, and RANK, and could differentiate into TRACP(+) multinucleate cells in the presence of soluble RANKL or TNF-alpha. RANKL-induced osteoclastogenesis gave a reduction of 20% in the progenitors from TRAF2-deficient mice compared with that of the cells from littermate wildtype mice, whereas TNF-alpha-induced osteoclastogenesis was severely impaired in the cells from the TRAF2-deficient mice. Only a few TRACP(+) multinucleate cells were formed, and TNF-alpha-mediated activation of JNK, NF-kappaB, and NFATc1 was defective. TRAF2 overexpression induced differentiation of osteoclast progenitors from wildtype mice into TRACP(+) multinucleate cells. These results suggest that TRAF2 plays an important role in TNF-alpha-induced osteoclastogenesis.

TRAF5 functions in both RANKL- and TNFalpha-induced osteoclastogenesis.

Although TRAF6 is essential for both RANKL- and TNFalpha-induced osteoclastogenesis, it has remained unclear whether other members of the TRAF family are involved in osteoclastogenesis. We examined TRAF5 function in both RANKL- and TNFalpha-induced osteoclastogenesis by using osteoclast progenitor cells from TRAF5-deficient mice. The results demonstrated that RANKL or TNFalpha did not effectively induce osteoclast differentiation from osteoclast progenitor cells derived from these mice into mature multinucleated osteoclasts, although c-jun N-terminal kinase (JNK) and NF-kappaB activation was apparently observed in osteoclast progenitor cells. In the parathyroid hormone (PTH)-induced hypercalcemia model, calcium concentration peaked at day 3 after administration. However, in TRAF5-deficient mice, this peak was delayed and found at day 5, showing less effective osteoclast differentiation. Thus, we have provided the first evidence showing that TRAF5 is involved in osteoclastogenesis.

Osteopetrosis and thalamic hypomyelinosis with synaptic degeneration in DAP12-deficient mice.

Deletions in the DAP12 gene in humans result in Nasu-Hakola disease, characterized by a combination of bone fractures and psychotic symptoms similar to schizophrenia, rapidly progressing to presenile dementia. However, it is not known why these disorders develop upon deficiency in DAP12, an immunoreceptor signal activator protein initially identified in the immune system. Here we show that DAP12-deficient (DAP12(-/-)) mice develop an increased bone mass (osteopetrosis) and a reduction of myelin (hypomyelinosis) accentuated in the thalamus. In vitro osteoclast induction from DAP12(-/-) bone marrow cells yielded immature cells with attenuated bone resorption activity. Moreover, immature oligodendrocytes were arrested in the vicinity of the thalamus, suggesting that the primary defects in DAP12(-/-) mice are the developmental arrest of osteoclasts and oligodendrocytes. In addition, the mutant mice also showed synaptic degeneration, impaired prepulse inhibition, which is commonly observed in several neuropsychiatric diseases in humans including schizophrenia, and aberrant electrophysiological profiles in the thalami. These results provide a molecular basis for a unique combination of skeletal and psychotic characteristics of Nasu-Hakola disease as well as for schizophrenia and presenile dementia.