ABSTRACT
Consider continuous real-valued time series observations yj, j = 1, 2, …, n, with finite variance and a smooth trend. Let be the residuals which have a cumulative distribution function F(tj, ·) that is a smooth but an arbitrary function of time. We address kernel estimation of F when the errors have long-memory correlations, using regression residuals and kernels that have absolutely integrable characteristic functions.
Acknowledgments
Remarks of two referees and the editor are gratefully acknowledged. The precipitation data used in this paper have been made available by the MeteoSchweiz, die Bundesamt für Meteorologie und Klimatologie, Switzerland. The earth surface temperature data are available through the homepage of the Met Office, UK.