报告主题：Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra

报告人：Saeid Rezakhah，副教授，阿米尔卡比尔理工大学（伊朗德黑兰）

照片：

邀请人：董从造

报告时间：2019年07月09日（周二）下午14:30-15:20

报告地点：南校区信远楼II206数统院会议室

报告人简介：

Saeid Rezakhah 是伊朗德黑兰阿米尔卡比尔理工大学副教授（stage 32），博士生导师，1996年取得英国伦敦大学玛丽皇后和韦斯特菲尔德学院（Queen Mary and Westfield College, University of London）概率统计博士学位，先后在美国密歇根州立大学和英国伦敦大学做访问教授。Saeid Rezakhah教授研究兴趣包括Selfsimilar Process; Hidden Markov Mixture models, Periodically Correlated Processes, Stable distributions, Random Polynomials; Time-Series Analysis; Stable Process和 Information Theory等等，目前在国际学术期刊发表sci检索论文30余篇。

报告摘要：

Imposing some flexible sampling scheme we provide some discretization of continuous discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time process. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also a new method for estimation time dependent Hurst parameter of such process is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S&P500 and Dow Jones indices for some special period.