  We propose parametric copulas that capture serial dependence in stationary
heteroskedastic time series. We develop our copula for first order Markov
series, and extend it to higher orders and multivariate series. We derive the
copula of a volatility proxy, based on which we propose new measures of
volatility dependence, including co-movement and spillover in multivariate
series. In general, these depend upon the marginal distributions of the series.
Using exchange rate returns, we show that the resulting copula models can
capture their marginal distributions more accurately than univariate and
multivariate GARCH models, and produce more accurate value at risk forecasts.
