High Dimensional Threshold Regression with Common Stochastic Trends

We study inference for threshold regression in the context of a large panel factor model with common stochastic trends. We develop a Least Squares estimator for the threshold level, deriving almost sure rates of convergence and proposing a novel, testing based, way of constructing confidence intervals. We also investigate the properties of the PC estimator for the loadings and common factors in both regimes, and develop a procedure to estimate the number of common trends in each regime. Our theoretical findings are corroborated through a comprehensive set of Monte Carlo experiments and an application to US mortality data