The Multivariate Empirical of Long Memory Processes

[摘要] We establish a functional central limit theorem for the empirical pro-cess of long range dependent stationary multivariate sequences under Gaussian subordination conditions. The proof is based upon a convergence result for cross-products of Hermite polynomials and a multivariate uniform reduction principle, as in Marinucci for bivariate sequences.

[关键词] Multivariate processes;Empirical process;Hermite polynomials;Convergence