Estimation and Testing for the Cointegration Rank in a Threshold Cointegrated System

The paper generalises estimation and inference procedures for a threshold VECM with more than one cointegrating relation. We derive estimators of long-run parameters and loading factors by means of a reduced rank regression. We provide their asymptotic distributions and propose a testing procedure for the cointegrating rank. The asymptotic distributions of our test statistics are derived and tabulated. In order to improve finite sample inference, we also compute bootstrap approximation to the distribution of our test statistics. Monte-Carlo experiments are conducted to evaluate the finite-sample performance of our test and its power. We apply our methodology to the expectations hypothesis of the term structure of U.S. interest rates.