We establish a functional central limit theorem for the empirical process of bivariate stationary long range dependent 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 Dehling and Taqqu [Ann. Statist. 17 (1989), 1767-1783] for the univariate case. The effect of estimated parameters is also discussed.
Marinucci, D. (2005). The empirical process for bivariate sequences with long memory. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES, 8(2), 205-223 [10.1007/s11203-004-2790-9].
The empirical process for bivariate sequences with long memory
MARINUCCI, DOMENICO
2005-01-01
Abstract
We establish a functional central limit theorem for the empirical process of bivariate stationary long range dependent 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 Dehling and Taqqu [Ann. Statist. 17 (1989), 1767-1783] for the univariate case. The effect of estimated parameters is also discussed.File in questo prodotto:
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