We present a data-driven framework to model the stochastic evolution of volume-price distribution from the New York Stock Exchange (NYSE) equities. The empirical distributions are sampled every 10 minutes over 976 trading days, and fitted to different models, namely Gamma, Inverse Gamma, Weibull, and Log-Normal distributions. Each of these models is parameterized by a shape parameter, $phi$, and a scale parameter, $θ$, which are detrended from their daily average behavior. The time series of the detrended parameters is analyzed using adaptive binning and regression-based extraction of the Kramers-Moyal (KM) coefficients, up to their sixth order, enabling to classification of its intrinsic dynamics. We show that (i) $φ$ is well described as a pure diffusion with a linear mean regression for the Gamma, Inverse Gamma, and Weibull models, while $θ$ shows dominant jump-diffusion dynamics, with an elevated fourth- and sixth-order moment contributions; (ii) the log-normal model shows however the opposite: $θ$ is predominantly diffusive, with $φ$ showing weak jump signatures; (iii) global moment inversion yields jump rates and amplitudes that account for a large share of total variance for $θ$, confirming that rare discontinuities dominate volatility.

翻译：摘要：我们提出了一种数据驱动框架，用于建模纽约证券交易所（NYSE）股票量价分布的随机演化过程。实证分布以每10分钟为间隔采样，覆盖976个交易日，并拟合为伽马分布、逆伽马分布、威布尔分布和对数正态分布等不同模型。每个模型均通过形状参数 \(\phi\) 和尺度参数 \(\theta\) 参数化，且这些参数经过日平均行为去趋势处理。采用自适应分箱与基于回归的克拉默-莫亚尔（KM）系数提取方法（最高至六阶），对去趋势参数的时间序列进行分析，从而对其内在动力学特征进行分类。结果表明：（i）对于伽马分布、逆伽马分布和威布尔分布，\(\phi\) 可视为带有线性均值回归的纯扩散过程，而 \(\theta\) 呈现显著的跳跃扩散动力学特征，且四阶与六阶矩贡献升高；（ii）对数正态模型则呈现相反现象：\(\theta\) 以扩散过程为主，\(\phi\) 仅表现出微弱跳跃特征；（iii）全局矩反演得出的跳跃速率与振幅可解释 \(\theta\) 总方差中的大部分比例，证实稀有不连续性主导了波动性。