Abstract: Herein, we use hybrid resampling to address (a) the long-standing problem of inference on change times and changed parameters in change-point ARX-GARCH models, and (b) the challenging problem of valid confidence intervals, after variable selection under sparsity assumptions, for the parameters in linear regression models with high-dimensional stochastic regressors and asymptotically stationary noise. For the latter problem, we introduce consistent estimators of the selected parameters and a resampling approach to overcome the inherent difficulties of post-selection condence intervals. For the former problem, we use a sequential Monte Carlo for the latent states (respresenting the change times and changed parameters) of a hidden Markov model. Asymptotic efficiency theory and simulation and empirical studies demonstrate the advantages of the proposed methods.

Key words and phrases: Change-point ARX-GARCH models, coverage probability of credible and confidence intervals, double block bootstrap, hidden Markov models and particle filters, sequential Monte Carlo, sparsity and variable selection.