Long- and short-range dependent sequences under exponential subordination
The authors investigate long-range dependent processes that can be obtained as instantaneous functionals of processes with exponential marginals. Let \((X_i)_{i\geq 1}\) and \((Y_i)_{i\geq 1}\) be two independent copies of a mean-zero Gaussian process with covariance function \(\rho(k)= L(k) k^{-\alpha/2}\), \(0< \alpha< 1\). Define \(Z_i= X_i^2+ Y_i^2\) and \(W_i= G(Z_i)\), where \(G\) is some \(L^2\)-function. The authors develop limit theory for partial sums of the \((W_i)_{i\geq 1}\)-process as well as for the empirical process. Results parallel to those developed earlier for instantaneous functionals of Gaussian processes are obtained [e.g. \textit{M. S. Taqqu}, Z. Wahrscheinlichkeitstheorie Verw. Geb. 50, 53-83 (1979; Zbl 0397.60028), \textit{H. Dehling} and \textit{M. S. Taqqu}, Ann. Stat. 17, No. 4, 1767-1783 (1989; Zbl 0696.60032)].
scientific article; zbMATH DE number 1310360
scientific article