4pm (Joint Nomura-OMI Seminar) - The Use of Randomness in Time Series Analysis

23 October 2014
Professor Piotr Fryzlewicz
This is an exploratory talk in which we describe different potential 
uses of randomness in time series analysis.

In the first part, we talk about Wild Binary Segmentation for change-point detection, where randomness is used as a device for sampling from the space of all possible contrasts (change-point detection statistics) in order to reduce the computational complexity from cubic to just over linear in the number of observations, without compromising on the accuracy of change-point estimates. We also discuss an interesting related measure of change-point certainty/importance, and extensions to more general nonparametric problems.

In the second part, we use random contemporaneous linear combinations of time series panel data coming from high-dimensional factor models and argue that this gives the effect of "compressively sensing" the components of the multivariate time series, often with not much loss of information but with reduction in the dimensionality of the model.

In the final part, we speculate on the use of random filtering in time series analysis. As an illustration, we show how the appropriate use of this device can reduce the problem of estimating changes in the autocovariance structure of the process to the problem of estimating changes in variance, the latter typically being an easier task.