Abstract: The characteristic of oil and gas as substitutes for each other makes the two show a certain correlation. The changes and linkage of oil and gas prices in the world's largest oil and gas consumer market will affect the global energy development pattern and investment strategy. Firstly, the paper studies the overall correlation between crude oil and natural gas yields in North America based on the Bayesian DCC-GARCH (Dynamic Conditional Correlation GARCH) model. In the case that the overall correlation between the two was less significant, the dynamic correlation characteristics of the two in trend, season and remainder are studied by STL decomposition. And then we analyze the nonlinear characteristics of correlation between oil and gas in trend through the LSTAR (Logistis Smooth Transformation Autoregressive) model. The results show the dynamic correlation between crude oil and natural gas yields in North American market is always positive, with a correlation range of[0.137,0.216] and a median of 0.181, the result of which could better reflect the time-varying characteristics of oil and gas linkage compared with the CCC-GARCH model (Constant Conditional Correlation GARCH). The correlation range of oil and gas is small, showing that there is no significant correlation between them. The results of STL decomposition show that there is a significant correlation between oil and gas yields in trend. And, LSTAR model could better characterize the correlation fluctuation and have a higher degree of fitting than AR model. The correlation between oil and gas in trend has a smooth transition at 2.026, and the transform speed from low zone to high zone is very fast. The results of the study have guiding significance for investors to increase their income, producers to control their costs, and the relevant government departments to formulate corresponding energy strategies.

Key words: crude oil, natural gas, linkage, trend, nonlinear