Detecting and estimating long-range dependence are important in the analysis of many environmental time series. This article proposes a periodogram roughness (PR) estimator and describes its uses for testing and estimating the dependence structure. Asymptotic critical values are generated for performing the test, and special attention is given to investigating the properties of the PR regarding size and power. The conventional short-memory models, such as the autoregressive (AR), are shown to be less parsimonious. Forecasting errors of both fractional Gaussian noise (FGN) and fractional autoregressive moving average (FARMA) are investigated by conducting simulation studies. In addition to the PR, maximum likelihood (ML) and semi-parametric (SP) estimators are used and evaluated. Our results have shown that more accurate forecasted points are obtained when using the fractional forecasting. The methods are illustrated using Swedish wind speed data. Copyright (C) 2004 John Wiley Sons, Ltd.