Abstract: As an extension of linear cointegration, threshold cointegration has been a vibrant research topic in finance and statistics. Existing estimation procedures of threshold cointegration are usually based on the threshold vector error correction model (TVECM); however, only one threshold cointegration is considered. In this paper, we investigate estimation of the multiple-threshold cointegration that is more widely used in application. Two proposed methods, the LSE and the Smoothed LSE are studied, via the multiple-regime TVECM. The convergence rate of the LSE is obtained and the limiting distribution of the smoothed LSE is developed. To assess the performance of these estimators, a simulation study was conducted, in which the results support the asymptotic theories. As an example, we study the term structure of interest rates by a two-threshold cointegration model.

Key words and phrases: Convergence rate, error correction model, multiple-threshold cointegration, smoothed least squares estimator, super consistency.