LASSO estimation of threshold autoregressive models

This paper develops a novel approach for estimating a threshold autoregressive (TAR) model with multiple-regimes and establishes its large sample properties. By reframing the problem in a regression variable selection context, a least absolute shrinkage and selection operator (LASSO) procedure is proposed to estimate a TAR model with an unknown number of thresholds, where the computation can be performed efficiently. It is further shown that the number and the location of the thresholds can be consistently estimated. A near optimal convergence rate of the threshold parameters is also established. Simulation studies are conducted to assess the performance in finite samples. The results are illustrated with an application to the quarterly US real GNP data over the period 1947-2009.