Abstract: Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this talk, I will demonstrate that a wide range of short-range dependent non-stationary and nonlinear time series can be well approximated globally by a white-noise-driven auto-regressive (AR) process of slowly diverging order. Uniform statistical inference of the latter AR structure will be discussed through a class of high dimensional L2 tests. I will further discuss applications of the AR approximation theory to globally optimal short-term forecasting, efficient estimation, and resampling inference under complex temporal dynamics.

 

 

Bio:Zhou Zhou obtained his Ph.D. in Statistics from the University of Chicago in 2009. He is currently a Full Professor at the Department of Statistical Sciences, University of Toronto. Zhou's major research interests lie in complex time series analysis, non- and semi- parametric inference, time-frequency analysis, change point analysis and functional and longitudinal data analysis.