On the use of the variogram in checking for independence in spatial data

The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow-up. An example is discussed.     

Non-stationary time series and the robustness of circadian rhythms

Circadian rhythms are regular oscillations in the value of behavioral and physiological variables of organisms that recur on a daily basis. The purpose of this study was to evaluate the extent of non-stationarity of circadian rhythms over several days, to determine how damaging is the violation of the assumption of stationarity in the analysis of circadian rhythms, and to formalize the concept of "rhythm robustness" as an index of oscillatory ("weak") stationarity. Simulated (computer-generated) and experimental data sets (rhythms of body temperature and running-wheel activity in several rodent species) were analysed. Tests of stationarity based on the variance of the daily means and the variance of the daily variances revealed that most experimental data sets are not stationary. Analysis of linear trends indicated that significant trends are rare in experimental data sets. Although the non-stationarity of the experimental data sets reduced the spectral energy of the Enright periodogram used to assess rhythmicity, detection of circadian rhythmicity was not prevented in any of the rhythmic data sets. The results of the various analyses allow the inference that, after high-frequency noise is filtered out, the value of the periodogram's Q(P) statistic reflects the extent of stationarity of the time series. Thus, the "robustness" of a circadian rhythm (i.e. the magnitude of the empirical Q(P) value as compared to the Q(P) value associated with a perfectly rhythmic time series) can serve as an index of the stationarity of the rhythm.     

Stationarity of climate-growth response is only marginally influenced by the soil moisture regime in Western Siberia

Stationary (time-stable) relationships between a tree-ring proxy and climatic drivers are a prerequisite for using tree rings as paleo-climatological archives, but non-stationarity has been detected worldwide. Here we use a classical, temperature-sensitive treeline site in Western Siberia to specifically test the influence of micro-site conditions (wet versus dry) on the stationarity of climate-growth relationships in three co-existing conifer species: Larix sibirica Ledeb., Picea obovata Ledeb., and Pinus sibirica DuTour. We test two commonly used tree-ring proxies, annual tree-ring width (TRW) and maximum latewood density (MXD), using moving windows and the bootstrapped transfer function stability test (BTFS). Summer temperature is the main driver of tree growth in all three species, but non-stationarities exist in all species and both tree-ring proxies. For TRW, we found stationarity only for larch from both micro-sites, while for MXD, we found stationarity for spruce from both micro-sites, and for pine from the wet micro-site. Micro-site variability did not seem to affect stationarity in any systematic way. We highlight the necessity to systematically test the influence of different methods of stationarity tests, since BTFS was more sensitive than moving-window analysis. Taken together, our results underscore the importance of testing the assumption of stationarity for diverse micro-sites, different species and proxies at all sites prior to any tree-ring based temperature reconstruction, since even within one site results can be drastically different.     

Substitutional bias confounds inference of cyanelle origins from sequence data

Summary Available molecular and biochemical data offer conflicting evidence for the origin of the cyanelle of Cyanophora paradoxa. We show that the similarity of cyanelle and green chloroplast sequences is probably a result of these two lineages independently developing the same pattern of directional nucleotide change (substitutional bias). This finding suggests caution should be exercised in the interpretation of nucleotide sequence analyses that appear to favor the view of a common endosymbiont for the cyanelle and chlorophyll-b-containing chloroplasts. The data and approaches needed to resolve the issue of cyanelle origins are discussed. Our findings also have general implications for phylogenetic inference under conditions where the base compositions (compositional bias) of the sequences analyzed differ. Offprint requests to: C.J. Howe     

Temporal Analogues to Spatial K Functions

In this article, the spatial statistic known as the K function is adapted for temporal processes and patterns. The (optimal) K-function estimator is used in a testing procedure to determine whether behavior patterns of exposed rats versus control rats are different. Specifically, the temporal analogue to the K function is given and an approximately optimal estimator is developed. Next, a testing procedure, to determine whether a group of point patterns is generated from complete temporal randomness, is given. Finally, a testing procedure, to compare pairwise two groups of point patterns to each other, is given. The testing procedures are illustrated with rat-behavior data from both a control-control experiment as well as an exposed-control experiment, where in the latter case a difference in behavior is known to exist.     

Assessment of the non-Gaussianity and non-linearity levels of simulated sEMG signals on stationary segments

The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered.A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5 s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test.The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR.     

Persistence of policy shocks to Ecological Footprint of the USA

This is the first study that aims to investigate policy shocks to Ecological Footprint of the USA. More precisely, we analyze the stochastic behaviors of the Ecological Footprint and its components (carbon Footprint, cropland, grazing land, forest products, built-up-land, and fishing grounds) by using Fourier unit root tests that are more powerful under an unknown number of breaks. The stationarity of a time series gives information about its future behavior based on past behavior. More specifically, stationarity properties give information on whether shocks have transitory or permanent effects on a variable; therefore, the stationarity of a time series has important implications to the formation of appropriate policies by decision makers. Stochastic properties of the Ecological Footprint are important considerations to the implementation of global and local policies targeting global warming, climate change and environmental degradation. Empirical results show that the Ecological Footprint is non-stationary which suggests that policies affecting the Ecological Footprint will have long-term and permanent effects. Findings and policy implications are further discussed.     

Analysis of the tennis racket vibrations during forehand drives: Selection of the mother wavelet

The time–frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time–frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25 ± 17%, 2 ± 5%, 5 ± 7% and 27 ± 27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable.