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SUMMARYHere we introduce a concept of periodogram roughness, which we use for estimating the roughness (variation) of spectral density. Periodogram roughness is used for several estimation and testing purposes. With the help of a spectral compensator factor it can be used to estimate fractional order as well as the autoregressive parameters or the moving average. The periodogram roughness is asymptotically normal when sample size increases. We applied our methods to temperature measurements in 10 network stations throughout Sweden to estimate the fractional order. The cycle pattern in temperature measurements has been tested. It shows long range dependency structure.

When infrared spectral data are used in classification and/or multivariate regression methods there can be problems related to both chemical understanding and computation speed due to the large number of wavenumbers in each spectrum. Here, it is shown that the Procrustes rotation technique can be used to select a minimum set of spectral variables (wavenumbers) to perform classification and regression. Procrustes rotation was coupled to several multivariate methods as PLS, SIMCA and potential curves (a maximum likelihood classification method). The practical problem of implementing a screening methodology for classifying apple juice-based beverages according to their contents of "pure" apple juice was addressed using attenuated total reflectance, mid-IR spectroscopy. It is found that two of the original wavenumbers are almost as good predictors as all the 176 initial ones.

SUMMARYDetecting 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.