Finite-sample power properties of threshold cointegration tests

Abstract

The empirical powers of recently proposed threshold cointegration tests are examined. Using an empirically realistic data generation process two crucial results are derived. First, relative to the implicitly symmetric Engle–Granger test, threshold cointegration tests lack power even in the presence of substantial asymmetry. Second, the use of consistent-threshold estimation to endogenise or optimize threshold selection is found to reduce the power of both threshold autoregressive and momentum threshold autoregressive cointegration tests. The implications of these findings are noted in light of the increased use of threshold cointegration tests in recent empirical research in economics and finance.

Notes

¹ In the interests of brevity, results are presented for a single sample size of T = 200. Further, near identical results for alternative sample sizes are available upon request. The required critical values at the 5% level of significance for the alternative tests are calculated via the standard approach of Monte Carlo simulation of two independent unit root processes over 50 000 replications.

² In the current analysis a threshold of zero is considered in the Monte Carlo analysis. Further results unreported here show that as the value of the threshold is increased there is an increase in power for all tests. Importantly however, there is no change in the ranking of the tests in terms of power. The observed increase in power has an intuitive explanation given the nature of the DGP employed as a higher (lower) value of the threshold forces increased use of the regime with a greater (lesser) degree of stationarity as denoted by the asymmetric adjustment parameter. A similar relationship between test power and the threshold value was noted by Pippenger and Goering (2000) in their analysis of the Phillips–Perron unit root test in the presence of EQ-, Band- and RD-TAR adjustment.