High Dimensional Threshold Factor Models with Common Stochastic Trends

We study inference for threshold regression in the context of a large 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 way of constructing confidence intervals based on a randomised test. Our confidence intervals are constructed using the rates of convergence of the estimated threshold level, and no limiting distribution is required. We also develop a procedure to estimate the number of common trends in each regime, and investigate the properties of the Principal Component estimator for the loadings and common factors in both regimes. Our theoretical findings are corroborated through a comprehensive set of Monte Carlo experiments, and an application to equity prices and bond yields.