英文标题：
《Asymptotic properties of maximum likelihood estimator for the growth
rate for a jump-type CIR process based on continuous time observations》
---
作者：
Matyas Barczy, Mohamed Ben Alaya, Ahmed Kebaier, Gyula Pap
---
最新提交年份：
2017
---
英文摘要：
We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to so-called basic affine jump-diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution, where the almost sure limit of an appropriately scaled jump-type supercritical CIR process comes into play. This is a new phenomenon, compared to the critical case, where a diffusion-type critical CIR process plays a role.
---
中文摘要：
我们考虑了一个由标准维纳过程和一个隶属函数驱动的跳跃型Cox—Ingersoll—Ross（CIR）过程，并研究了其增长率的极大似然估计（MLE）的渐近性质。我们区分了三种情况：亚临界、临界和超临界。在亚临界情况下，我们证明了弱相合性和渐近正态性，并且在附加矩假设下，证明了强相合性。在超临界情况下，我们证明了强相合性和混合正态（但非正态）渐近行为，而在临界情况下，我们描述了弱相合性和非标准渐近行为。我们将我们的结果专门化为所谓的基本仿射跳跃扩散。关于超临界情况下的极大似然估计的渐近行为，我们导出了极限混合正态分布的随机表示，其中适当比例的跳跃型超临界CIR过程的几乎确定极限起作用。与临界情况相比，这是一种新现象，在临界情况下，扩散型临界CIR过程起作用。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
PDF下载：
-->