Estimation of the dependence parameter in linear regression with long-range-dependent errors (Q1965876)

The authors establish the consistency and root-n asymptotic normality of the exact maximum likehood estimator of the dependence parameter in linear regression models where the errors are a nondecreasing function of a long-range-dependent Gaussian process. The spectral density of the Gaussian process is supposed to be unbounded at the origin. This paper generalizes some of the results of \textit{R. Dahlhaus} [Ann. Stat. 17, No. 4, 1749-1766 (1989; Zbl 0703.62091)] to linear regression models with non-Gaussian long-range-dependent errors.