报告题目：Maximum likelihood estimation for α-stable double autoregressive models

报告时间：2022年07月13日，星期三，15:00—18：00

腾讯会议ID：103-881-319

报告人：李东副教授，清华大学统计学研究中心

报告简介：The talk investigates maximum likelihood estimation (MLE) for a first-order double autoregressive model with standardized non-Gaussian symmetric α-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 location is always asymptotically normal, regardless of stationary or explosive case. This point totally differs from that for linear AR models in Andrews, Calder and Davis (2009). Furthermore, it is the first time to provide exact values of the quantities related to the innovation in the asymptotic covariance matrices when the true innovation is the standard Cauchy distribution. Additionally, a Kolmogorov-type test statistic is proposed for model diagnostic checking in the stationary case and its modified version is also considered in finite samples. Monte Carlo simulation studies are conducted to confirm our theoretical findings and assess the finite-sample performance of the MLE and the modified Kolmogorov-type test. 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，2005年毕业于中科院数学与系统科学研究院；2011年毕业于香港科技大学，随后在美国爱荷华大学统计与精算系从事博士后研究；2013年加入清华大学。主要研究兴趣：非线性非平稳时间序列分析、矩阵值时间序列分析、机器学习、金融计量学、网络数据分析、空间统计等。