发表机构
Université de Sousse, Laboratoire LAMMDA, École Supérieure des Sciences et de Technologie de Hammam Sousse（苏塞大学，LAMMDA实验室，哈马姆苏塞高等科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出遍历基本仿射跳跃扩散模型的随机效应扩展，用经验跳跃频率估计个体跳跃强度，再以伯恩斯坦多项式估计其共同密度，并推导渐近性质，模拟和实证验证了方法。
AI 中文摘要
本文针对一群独立轨迹的总体，提出了一种遍历基本仿射跳跃扩散（BAJD）模型的随机效应扩展，其中每个轨迹具有个体未观测的跳跃强度和共同的结构参数。在连续时间观测下，每个强度通过经验跳跃频率进行估计。我们建立了该估计量在观测时间范围趋于无穷时的强一致性和稳定混合正态极限。随后，估计的强度被用作伪观测值，以构造其共同密度的伯恩斯坦多项式估计量。在序贯渐近框架下，推导了该估计量的偏差、方差、均方积分误差以及逐点渐近正态性。该理论适用于具有有限活动的通用正跳跃大小分布，并专门针对Gamma$(k,\lambda)$族进行了细化，包括指数和厄兰情形。对于该族，我们推导了共同速率参数的合并估计量，并建立了其一致性、渐近正态性以及与个体强度估计量的一阶条件渐近独立性。我们还提出了一种总体平稳均值的相合插入估计量。通过模拟和对金融已实现波动率数据的实证应用，对该方法进行了说明。
英文摘要
This paper develops a random-effects extension of the ergodic basic affine jump-diffusion (BAJD) model for a population of independent trajectories with individual unobserved jump intensities and common structural parameters. Under continuous-time observation, each intensity is estimated by the empirical jump frequency. We establish the strong consistency and stable mixed-normal limit of this estimator as the observation horizon tends to infinity. The estimated intensities are then used as pseudo-observations to construct a Bernstein-polynomial estimator of their common density. Its bias, variance, mean integrated squared error, and pointwise asymptotic normality are derived under a sequential asymptotic framework. The theory is developed for general positive jump-size distributions with finite activity and specialized to the Gamma$(k,λ)$ family, including the exponential and Erlang cases. For this family, we derive a pooled estimator of the common rate parameter and establish its consistency, asymptotic normality, and first-order conditional asymptotic independence from the individual intensity estimators. We also propose a consistent plug-in estimator of the population stationary mean. The methodology is illustrated through simulations and an empirical application to financial realized-volatility data.
