The nonlinear dynamic relationship between crude oil price and stock markets for the selected eight Asia-Pacific economies from 1997/07/01 to 2013/07/01 is investigated. In the traditional threshold regime switching models framework, the optimization is complicated in the procedure of parameter estimation and the identification of unknown nuisance parameters is more difficult. Therefore, a Bayesian threshold regime switching cointegration approach is implemented instead in this study. Based on Bayesian MCMC algorithm, It is found that there is threshold regime switching cointegrating relationship between crude oil and Korea stock market, and between crude oil and Malaysia stock market. The results suggest that there exist asymmetric adjustments in oil-Korea stock market nexus and oil-Malaysia stock market nexus. On the other hand, there are no asymmetric adjustments between oil and Japan, Australia, South Korea, India, Indonesia and Singapore stock markets. The regime switching cointegration analysis could provide a different view to the relationship between crude oil price and Asia-Pacific stock markets.
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