Title: Inference for location of change points in high-dimensional non-stationary vector auto-regressive models
Authors: Abolfazl Safikhani - University of Florida (United States) [presenting]
Abstract: Piece-wise stationary Vector Auto-Regressive models (VAR) are among the well-known and useful models in time series analysis. Existing methods provide sub-optimal estimators to detect the location of change/breakpoints in high-dimensional VAR models due to the existence of terms such as total sparsity of transition matrices and the logarithm of the number of time series components in the consistency rate. We study a refitted least squares estimator for change point parameters in high-dimensional VAR models with sparse model parameters. We show that the newly defined estimator reaches an optimal rate of convergence and the corresponding rate for relative location of change points reaches $O(1/T)$ for certain non-vanishing jump sizes, where $T$ is the sample size. Further, the limiting distribution of the proposed estimate is obtained under both vanishing and non-vanishing jump sizes, thereby allowing the construction of confidence intervals for change point parameters. The proposed methodology is tested empirically over different synthetic data sets while an application to analyzing an EEG data set is also provided.