Abstract
This paper proposes and estimates a statistical model of nonlinear cointegration, with applications to the stock markets of Japan and the United States. 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) [1] to stock price ratio variables, both upward and downward divergent bubble processes are estimated at a time. We conclude that, although two stock price indexes are not linearly cointegrated, they are considered to be cointegrated nonlinearly.
Highlights
In this paper we propose and develop the recursive estimation method of a nonlinear statistical model of speculative bubbles and utilize this model in establishing an idea of nonlinear cointegration
We apply this idea to the stock market indexes of Japan and the United States, and we detect how these indexes commove in the long run they deviate from the long-run relationship nonlinearly in the short run
What we propose in this paper is a statistical model that incorporates latent cointegration relationship not linearly but nonlinearly
Summary
In this paper we propose and develop the recursive estimation method of a nonlinear statistical model of speculative bubbles and utilize this model in establishing an idea of nonlinear cointegration We apply this idea to the stock market indexes of Japan and the United States, and we detect how these indexes commove in the long run they deviate from the long-run relationship nonlinearly in the short run. Zhang and Liu (2014) [3] conduct linear cointegration test among any pair of Japan, the United States and China and reach the conclusion that the linear cointegration is rejected This is the origin of our analysis here because our daily observation suggests that the worldwide stock markets commove at any rate.
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