Weak convergence of the sequential empirical copula processes under long-range dependence
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We consider nonparametric estimation for multivariate copula-based stationary time-series models under long-range dependence, where the observed time series are subordinated to the long-memory stationary Gaussian processes and characterized by arbitrary marginal distributions and parametric copula function. We establish the limit theorems for the marginal and quantile marginal empirical processes and study the weak convergence of the sequential empirical copula processes under Gaussian subordination. The result of the limiting processes in the case of long-memory is quite different from the limiting distributions of i.i.d. and weakly dependent cases. Furthermore, we construct and simulate Gausian and Clayton copulas under short and long-memories.
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