This paper proposes and estimates a statistical model of nonlinear cointegration with applications to the stock markets of Japan, United States, and China. We define nonlinear cointegration as a long-run stable relationship between two time series variables even in the presence of temporary nonlinear divergence from this long-run relationship. More concretely, extending the bubble model of Asako and Liu (2013) to stock price ratio variables, both upward and downward divergent bubble processes are estimated at a time. We conclude that, although no pair of stock price series among the three is linearly cointegrated, they are considered to be cointegrated nonlinearly.
