Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
The study initiates a theoretical analysis of dynamic benchmarking models.
problem Lack of theoretical foundation and empirical studies in dynamic benchmarks.
method Examined two realizations of dynamic benchmarking: sequential and hierarchical dependency models.
result Sequential dynamic benchmarks show initial performance improvement but can stall after three rounds due to label noise.
Generic model for commodity derivatives pricing.
problem Modeling forward curves in commodity derivatives.
method Theoretical demonstration of multiple components driving commodity prices; empirical validation.
result Model accurately prices commodity derivatives, close to market prices.
There is more and more empirical evidence that multifractality constitutes another and perhaps the most significant financial stylized fact. A realistic model of the financial dynamics should therefore incorporate this effect. The most promising in this respect is the Multifractal Model of Asset Returns (MMAR) introduc…
In the present paper, a fuzzy logic based method is combined with wavelet decomposition to develop a step-by-step dynamic hybrid model for the estimation of financial time series. Empirical tests on fuzzy regression, wavelet decomposition as well as the new hybrid model are conducted on the well known SP500 index fin…
Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.
problem Stability and accuracy in neural nets modeling stochastic dynamics with many parameters.
method Three steps: probabilistic weights, partial knowledge incorporation, and PAC-Bayesian training.
result Improved model fit with partial and noisy prior knowledge.
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possi…
The paper analyzes the training dynamics of neural networks using kernel methods.
problem Understanding the training dynamics of neural networks in high-dimensional settings.
method High-dimensional asymptotics and gradient flow on kernel least-squares objectives.
result The training dynamics of neural networks undergo three stages, characterized by behaviors in the Oracle and Empirical worlds.
Continuous-time model shows insider trading constraints impact market dynamics.
problem Trading constraints faced by insiders in continuous-time models.
method Proved global existence of equilibrium with terminal trading constraint.
result Equilibrium model aligns with empirical market behaviors.
Novel model captures high-dimensional copulas with spectral dynamics and regularization.
problem Modeling time-varying, asymmetric, tail-dependent copulas in high dimensions.
method Score-driven dynamics for eigenvalues, non-linear shrinkage for biases, parsimonious and scalable.
result Model outperforms recent alternatives in capturing co-movements and diversification potential.
This paper analyzes how diffusion models learn and generalize concepts.
problem Learning and generalizing concepts in compositional data-generating processes.
method Introduced a structured identity mapping (SIM) task to analyze neural network learning dynamics.
result SIM task captures key empirical observations on compositional generalization.
The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlat…
Model predicts bid and ask price dynamics with spread-dependent intensities.
problem Predicting bid and ask price dynamics in high-frequency stock markets.
method Extended Hawkes process with zero intensities, spread-dependent intensities, and negative excitement.
result Spread-narrowing tendency, excitations caused by previous events, impact of flash crashes, and different market participant features.
Study on liquidity dynamics in Uniswap v3 pools using statistical methods.
problem Characterize liquidity in Uniswap v3 pools.
method Functional principal component analysis (FPCA) and dynamic factor methods.
result Liquidity dynamics in Uniswap v3 pools are well-captured by a low-order Legendre polynomial basis.
The study improves VaR forecast accuracy by modeling conditional quantile dynamics.
problem Improving the accuracy of Value-at-Risk (VaR) forecasts for time-varying quantiles.
method Time-varying modeling of VaR, evaluation via simulation, asymmetric Mean Absolute Deviation loss function.
result Substantial improvements in forecasting conditional quantiles by maintaining predicted quantile unchanged.
Stylized facts of empirical assets log-returns Z include the existence of (semi) heavy tailed distributions fZ(z) and a non-linear spectrum of Hurst exponents τ(β). Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is…
Attention-only transformers learn from context via two stages of inference.
problem Learning from corrupted token sequences in minimal transformers.
method Two-stage empirical Bayes interpretation: kernel-weighted posterior mean and particle dynamics.
result Effective denoising without explicit noise schedules, showing posterior-mean recovery under asymptotic conditions.
This article outlines a method for automatically generating models of dynamic decision-making that both have strong predictive power and are interpretable in human terms. This is useful for designing empirically grounded agent-based simulations and for gaining direct insight into observed dynamic processes. We use an e…
Predicting keywords performance, such as number of impressions, click-through rate (CTR), conversion rate (CVR), revenue per click (RPC), and cost per click (CPC), is critical for sponsored search in the online advertising industry. An interesting phenomenon is that, despite the size of the overall data, the data are v…
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.
A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. …
Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a sing…
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 m…
Gradient flow in softmax models tends to produce low-entropy outputs.
problem Understanding the training dynamics of softmax-based models.
method Analysis of gradient flow dynamics in the value-softmax model.
result Gradient flow drives optimization towards low-entropy solutions.
Study L2 regularization in deep networks, uncovering performance relations and proposing a training schedule.
problem Understanding and optimizing L2 regularization in deep learning models. method Empirical observations and theoretical analysis of gradient flow dynamics in infinitely wide networks.
result Empirical relations between model performance, L2 coefficient, learning rate, and training steps; optimal regularization parameter prediction; improved training schedule. We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…
Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.
problem Signal recovery from generative priors in compressed sensing.
method Stochastic Gradient Langevin Dynamics (SGLD) for signal recovery.
result SGLD converges to the true signal under mild assumptions on the generative model.
Many learning agents impact a financial market model, showing complex dynamics.
problem Understanding the dynamics of financial markets with multiple learning agents.
method Agent-based model of financial market with multiple reinforcement learning agents interacting.
result Inclusion of learning agents changes market dynamics to match empirical data.
This study explains RL training dynamics in LLMs, focusing on token-level optimization and reasoning pattern reshaping.
problem Understanding the training dynamics of RL in LLMs to improve their reasoning capabilities.
method Empirical analysis and theoretical modeling of RL training process, focusing on reasoning patterns and token optimization.
result RL primarily optimizes a sparse subset of critical tokens, reshaping reasoning pattern distributions and affecting model performance.
We propose a diffusion process to describe the global dynamic evolution of credit operations at a national level given observed operations at a subnational level in a sovereign country. Empirical analysis with a unique dataset from Brazilian federate constituents supports the conclusions. Despite the heterogeneity obse…
New model analyzes dynamic correlations in stock returns.
problem Analyzing time-varying correlations in high-dimensional data.
method Dynamic factor correlation model with novel parametrization.
result Model accurately captures heterogeneous heavy-tailed distributions and dependent shocks.
The paper analyzes the mean field Langevin dynamics and its convergence rate.
problem The convergence property of the mean field Langevin dynamics in the context of neural networks.
method The analysis uses a proximal Gibbs distribution and techniques from convex optimization.
result A concise convergence rate analysis of the mean field Langevin dynamics in both continuous and discrete time settings.
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affe…
This paper examines how Higher-Order Langevin Dynamics reduces memorization in diffusion models.
problem Memorization of training samples in diffusion models, violating copyright and privacy.
method Introduces Higher-Order Langevin Dynamics (HOLD) to regularize diffusion model trajectories.
result The dynamics of the data variable in HOLD are governed by a low-pass-filtered version of the learned score function, with smoothness increasing with model order.
The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential U under the influence of the variable noise intensity, dependin…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price,…
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total a…
Study local geometry of mixture models via spectral theory, revealing transitions in training dynamics.
problem Understanding the local geometry of high-dimensional mixture models.
method Spectral theory of Hessian and information matrices, focusing on i.i.d. Gaussian mixtures.
result Exact formulas for limits of spectral distribution and outlier eigenvalues, connecting training dynamics to effective dynamics.
New framework for online control in evolving populations.
problem Control of evolving populations in real-world conditions.
method Online control framework for linear and non-linear dynamical systems.
result Near-optimal regret bounds for gradient-based controllers.
Algorithm selects best model based on state, reducing costs.
problem Choosing the best model among many in different states of the world.
method Reinforcement learning algorithm to estimate optimal policy.
result Algorithm consistently selects optimal model based on covariates.
Paper proposes a method to estimate multiple dynamic quantiles jointly.
problem Limited joint estimation of multiple dynamic quantiles.
method Introduces a crossing penalty objective function for joint estimation.
result Validation through Monte Carlo experiments and empirical application on FTSE100 shows effectiveness.
Study designs incentives for adapting multi-agent systems without knowing their learning dynamics.
problem Designing incentives for an adapting population in multi-agent systems without prior knowledge of their learning dynamics.
method Introduces a model-based non-episodic Reinforcement Learning (RL) formulation for steering Markovian agents towards desired policies, focusing on history-dependent strategies to handle model uncertainty.
result Identifies conditions for the existence of steering strategies to guide agents to desired policies and provides empirical algorithms to approximately solve the objective.
Dynamic model improves static economics by incorporating time effects.
problem Static economics overlooks time-dependent phenomena, limiting model accuracy.
method Signals-based approach to reinterpret microeconomic theory, using utility function.
result Dynamic models provide better comparisons with empirical observations.
A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick structures of equities. We examine the impact of jump in price dynamics to the futu…
Auto-regressive models learn latent states from partially observed linear dynamical systems.
problem Understanding how auto-regressive models learn latent representations from partially observed linear dynamical systems.
method Empirical risk minimization on partially observed linear dynamical systems.
result Two-layer linear auto-regressive models learn to approximate Kalman filtering, coinciding with optimal state estimates.
This work studies learning dynamics in SSMs, linking them to deep linear networks.
problem Lack of theoretical understanding of SSMs, especially in deep state spaces.
method Analyzes learning dynamics of linear SSMs, focusing on frequency domain, and establishes links to deep linear networks.
result Analytical solutions for SSM learning dynamics under mild assumptions, linking to deep linear networks.