This study extends the threshold error-correction model of Enders and Siklos (2001) to the momentum threshold error-correction model with the dynamic conditional correlation GARCH model of Engle (2002), in order to investigate the asymmetric cointegration and causal relationships between the FTSE4GOOD index and the U.S. stock index. The results reveal that the responsible investment index and stock indexes adjust asymmetrically back to the long-run equilibrium relationship. Consequently, the stock index has a dominant impact on the responsible investment index and such a finding could prove valuable to investors when forecasting the responsible investment index.