Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes
Abstract
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.
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BibTeX
@misc{fathallah2026random,
title = {{Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes}},
author = {Hamdi Fathallah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05567},
eprint = {2609.05567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05567},
}
RIS
TY - UNPB
TI - Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes
AU - Hamdi Fathallah
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.05567
UR - https://arxiv.org/abs/2609.05567
AB - 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.
ER -