In this paper we revisit a time series model introduced by McElroy and Politis (2007a) and generalize it in several ways to encompass a wider class of stationary, nonlinear, heavy-tailed time series with long memory. The joint asymptotic distribution for the sample mean and sample variance under the extended model is derived; the associated convergence rates are found to depend crucially on the tail thickness and long memory parameter. A self-normalized sample mean, that concurrently captures the tail and memory behavior, is defined. Its asymptotic distribution is approximated by subsampling without the knowledge of tail or/and memory parameters; a result of independent interest regarding subsampling consistency for certain long-range dependent processes is provided. The subsampling-based confidence intervals for the process mean are shown to have good empirical coverage rates in a simulation study. The influence of block size on the coverage and the performance of a data-driven rule for block size selection are assessed. The methodology is further applied to the series of packet-counts from Ethernet traffic traces.

Forest canopies create dynamic light environments in their understorey, where spectral composition changes among patterns of shade and sunflecks, and through the seasons with canopy phenology and sun angle. Plants use spectral composition as a cue to adjust their growth strategy for optimal resource use. Quantifying the ever‐changing nature of the understorey light environment is technically challenging with respect to data collection. Thus, to capture the simultaneous variation occurring in multiple regions of the solar spectrum, we recorded spectral irradiance from forest understoreys over the wavelength range 300–800 nm using an array spectroradiometer. It is also methodologically challenging to analyze solar spectra because of their multi‐scale nature and multivariate lay‐out. To compare spectra, we therefore used a novel method termed thick pen transform (TPT), which is simple and visually interpretable. This enabled us to show that sunlight position in the forest understorey (i.e., shade, semi‐shade, or sunfleck) was the most important factor in determining shape similarity of spectral irradiance. Likewise, the contributions of stand identity and time of year could be distinguished. Spectra from sunflecks were consistently the most similar, irrespective of differences in global irradiance. On average, the degree of cross‐dependence increased with increasing scale, sometimes shifting from negative (dissimilar) to positive (similar) values. We conclude that the interplay of sunlight position, stand identity, and date cannot be ignored when quantifying and comparing spectral composition in forest understoreys. Technological advances mean that array spectroradiometers, which can record spectra contiguously over very short time intervals, are being widely adopted, not only to measure irradiance under pollution, clouds, atmospheric changes, and in biological systems, but also spectral changes at small scales in the photonics industry. We consider that TPT is an applicable method for spectral analysis in any field and can be a useful tool to analyze large datasets in general.

[1] A wavelet-based method of computing an index of storm activity is put forward. The new index can be computed automatically using statistical procedures and does not require selecting quiet days and removing the secular component by polynomial fitting. This 1-min index is designed to facilitate the study of the fine structure of geomagnetic storm events and requires only the most recent magnetogram records, e.g., the 2 months including the storm event of interest. It can thus be computed over a moving window as soon as new magnetogram records become available. Averaged over 1-hour periods, it is practically indistinguishable from the standard Dst index.

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