ECE Seminar: Learning from Heterogeneous Vector Time Series

I will first say a few words about the research activities of my team at Harvard. Then I will focus on some of our activities in the area of applied statistics and data analysis.
Starting with vector time series data, we will discuss the modeling by AR models. The Cohn Polytope plays a central intuitive role here--in the sense that hypothesis testing on the Cohn Polytope provides insights for our approach (although the proof of our results are fundamentally different). This intuition will be applied to order selection for an autoregressive model fitted to time series data, motivating a new information criterion that is provably consistent in specified, and asymptotically efficient in mis-specified settings. We then discuss extensions to multi-AR models where our model selection method can be intuitively explained by statistical analysis on Cohn manifolds with provable results. We then discuss further extensions to non-linear models.
I will then discuss our new statistical tests for local-stationarity that can be used for applying the above results to real data. I will also discuss inference and rare event prediction based on an amalgam of our approach with those of extreme value theory.
Applications to real data (e.g. financial and environmental data) will be presented demonstrating the power of our theories.

Vahid Tarokh is a Perkins Professor of Applied Mathematics and Hammond Vinton Hayes Senior Research Fellow in Electrical Engineering at Harvard University.