Abstract
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.
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