报告题目：Maximum likelihood estimation for $\alpha$-stable double autoregressive models

报 告 人：李东 副教授 清华大学

报告时间：2021年10月28日 上午 10:00-11:00

报告地点：腾讯会议  ID：875 622 657

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校内联系人：赵世舜 zhaoss@jlu.edu.cn

报告摘要：The paper investigates maximum likelihood estimation (MLE) for a first-order double autoregressive model with standardized non-Gaussian symmetric $\alpha$-stable innovation (sDAR) within a unified framework of stationary and explosive cases.  It is shown that the MLE of all parameters, including the stable exponent in the innovation, are strongly consistent and asymptotically normal (excluding the intercept for the explosive case). Particularly, the MLE of the parameter in the conditional mean is always asymptotically normal, regardless of stationary or explosive case. This point totally differs from that for linear AR models in \cite{acb}. It is the first time to provide exact values of the quantities related to the innovation in asymptotic covariance matrices when the true innovation is the standard Cauchy distribution. Additionally, a Kolmogorov-type test statistic is proposed for model diagnostic checking. Monte Carlo simulation studies are conducted to confirm our theoretical findings and assess the performance of the MLE and the diagnostic test statistic in finite samples. An empirical example is analyzed to illustrate the usefulness of sDAR models.

报告人简介：李东，清华大学统计学研究中心长聘副教授，2010年毕业于香港科技大学，2013年加入清华大学。主要研究兴趣：非线性时间序列分析，金融计量学，网络数据分析与大数据。目前担任全国工业统计学教学研究会常务理事，中国青年统计学家协会常务理事，北京大数据协会常务理事，中国概率统计学会副秘书长，中国现场统计研究会计算统计分会理事，北京应用统计学会理事。主持国家自然科学基金委面上项目2项；结题青年基金项目1项。