High-dimensional statistical learning for nonlinear time series

This thesis studies nonlinear time series data segmentation through high-dimensional statistical learning. In terms of time series segmentation, a procedure based on the sparse group Lasso jointly with clustering analysis and forward selection is developed to simultaneously locate and estimate structural break points in the autoregressive coefficients of piecewise autoregressive processes. In terms of the field of general high-dimensional statistical learning, I establish new properties under a general high-dimensional sparse regression framework, focusing on feature selection methods for highly correlated variables.