应数学系邀请，浙江大学庞天晓博士将于近日来公司进行讲学活动，欢迎感兴趣的师生参加！

报告时间：4月25日15:30

报告地点：数学系会议室（格物楼503）

报告题目：Structural Change in Non-stationary AR(1) Models

报告摘要： This talk revisits the asymptotic inference for non-stationary AR(1) models of Phillips and Magdalinos (2007, Journal of Econometrics) by incorporating a possible structural change in the AR parameter at an unknown time $k_{0}$. Consider the model $y_{t}=/beta_{1}y_{t-1}I/{t/leq k_0/}+/beta_2 y_{t-1}I/{t>k_0/}+ /varepsilon_{t},~t=1,2,/cdots ,T,$ where $I/{/cdot /}$ denotes the indicator function and one of $/beta_{1}$ and $/beta_{2}$ depends on the sample size $T$ and the other is equal to one. We examine four cases: Case (I): $/beta_{1}=/beta_{1T}=1-c/{k_{T}}$, $/beta_{2}=1$; (II):~$/beta_{1}=1$, $/beta_{2}=/beta_{2T}=1-c/{k_{T}}$,(III): $/beta_{1}=1$, $/beta_{2}=/beta_{2T}=1+c/{k_{T}}$, and case (IV):~$/beta_{1}=/beta_{1T}=1+c/{k_{T}}$, $/beta_{2}=1$, where $c$ is a fixed positive constant and $k_{T}$ is a sequence of positive constants increasing to $/infty $ such that $k_{T}=o(T)$. In addition, we assume that $/{/varepsilon_{t},t/geq 1/}$ is a sequence of i.i.d. random variables which are in the domain of attraction of the normal law (DAN) with zero means and possibly infinite variances. We derive the limiting distributions of the least squares estimators of $/beta_{1}$ and $/beta_{2}$ and that of the change-point estimator for the aforementioned cases under some mild conditions. It is shown that: (1) the asymptotic properties of the least squares estimator of the second AR parameter in mildly explosive AR(1) model with an unknown change point are very different from those in mildly explosive AR(1) model or unit root model without a change point; (2) when a unit root model switches to a mildly integrated or mildly explosive AR(1) model at time $k_{0}$, the asymptotic properties of the least squares estimator of $k_{0}$ remain the same, and the phase transition for the estimation error of $k_{0}$ occurs when $k_{T}$ has the same order of magnitude as $/sqrt{T}$. Monte Carlo simulations are conducted to examine the finite-sample properties of the estimators.

报告人简介：

庞天晓博士、副教授， 2000年本科毕业于浙江大学数学系统计学专业，2005年博士毕业于浙江大学数学系。2006.7-2007.7 台湾中央研究院和台湾中央大学博士后；2011.12-2012.12 美国耶鲁大学统计系访问学者。研究方向：概率极限理论，统计大样本理论。已发表相关学术论文20余篇。