The widely used models associated with copulas usually fall in the time-invariant framework where the parameters in copulas do not change through time. Recently, time-varying copulas whose parameters are driven by lagged variables and past observations have attracted considerable attention. This paper examines the dynamic dependence between crude oil and natural gas return rates by time-varying copulas including geometric copulas. West Texas Intermediate (WTI) crude oil and New York Harbor (NYH) natural gas daily prices over the period January 3, 2006 to December 30, 2016 is analyzed. The marginal models are specified as AR(p)-GJR-GARCH(P,Q)-skewed-t models. The performance of time-varying copulas and time-invariant copulas is demonstrated. According to Bayesian Information Criterion, time-varying rotated geometric Gumbel copula performs the best.

与系动词相关的广泛使用的模型通常落入时不变框架，其中系动词的参数不会随时间变化。近来，时变的copulas参数由滞后变量驱动，并且过去的观察结果引起了极大的关注。本文通过包括几何copulas在内的时变copulas检验原油和天然气回输率之间的动态相关性。分析了2006年1月3日至2016年12月30日期间的西德克萨斯中质（WTI）原油和纽约港（NYH）天然气的每日价格。边际模型指定为AR（p）-GJR-GARCH（P，Q）-skewed-t模型。证明了随时间变化的copulas和随时间变化的copulas的性能。根据贝叶斯信息准则，随时间变化的旋转几何Gumbel copula表现最佳。