In this talk, I will discuss two projects. Firstly, I propose novel statistical methods that detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. The methods allow for estimation of both the time of change in the network structure and the graph between each pair of change points, without prior knowledge of the number or location of the change points. Permutation and bootstrapping techniques are used to perform inference on the change points. The methods are applied to various simulated high dimensional data sets as well as to a resting state functional magnetic resonance imaging (fMRI) data set. The methods promise to offer a deep insight into the large-scale characterizations and functional dynamics of the brain. Extensions of the methods are also discussed. Secondly, I introduce the extremogram, which is a flexible quantitative tool that measures various types of extremal dependence in a stationary time series. Credible confidence bands are constructed for the extremogram using the stationary bootstrap. The cross-extremogram which measures cross-sectional extremal dependence in multivariate time series is also discussed. The use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated in several univariate and multivariate time series examples from finance and economics.
N.B. This talk is suitable for non-experts as well as students.