Efficient inference in multivariate fractionally integrated time series models

Summary A computationally simple maximum likelihood procedure for multivariate fractionally integrated time series models is introduced. This allows, e.g., efficient estimation of the memory parameters of fractional models or efficient testing of the hypothesis that two or more series are integrated of the same possibly fractional order. In particular, we show the existence of a local time domain maximum likelihood estimator and its asymptotic normality, and under Gaussianity asymptotic efficiency. The likelihood‐based test statistics (Wald, likelihood ratio and Lagrange multiplier) are derived and shown to be asymptotically equivalent and chi‐squared distributed under local alternatives, and under Gaussianity locally most powerful. The finite sample properties of the likelihood ratio test are evaluated by Monte Carlo experiments, which show that rejection frequencies are very close to the asymptotic local power for samples as small as n= 100 .     

The stationarity bias in research on the environmental determinants of health

An implicit assumption often made in research on the environmental determinants of health is that the relationships between environmental factors and their health effects are stable over space and time. This is the assumption of stationarity. The health impacts of environmental factors, however, may vary not only over space and time but also over the value ranges of the environmental factors under investigation. Few studies to date have examined how often the stationarity assumption is violated and when violated, to what extent findings might be misleading. Using selected studies as examples, this paper explores how the stationarity assumption can lead to misleading conclusions about health-environment relationships that may in turn have serious health consequences or policy implications. It encourages researchers to embrace nonstationarity and recognize its meaning because it helps direct our attention to the ignored factors or processes that may enhance our understanding of the phenomena under investigation.     

A Nonstationarity Test for the Spectral Analysis of Physiological Time Series with an Application to Respiratory Sinus Arrhythmia

The spectral analysis of time series requires the signal to be at least weakly stationary; i.e., the mean, (co-) variance, and spectrum of the time series should not vary from segment to segment. It is commonly assumed that psychophysiological time series are not stationary. This study introduces a nonstationarity test to the psychophysiological literature, which is derived from evolutionary spectral analysis. Basically, the test consists of a double window technique in both the time and frequency domains, leading to a two-way analysis of variance for times and frequencies. In the current study, the nonstationarity test is applied to heart rate data obtained in a typical psychophysiological setting. Heart rate and respiration were measured in four age groups under four conditions--rest, paced breathing, vigilance, and reaction time. The results indicate that only few physiological time series were completely stationary. However, for every subject, and in every condition stationary stretches could be found that were long enough to apply spectral analysis. Spectral measures (power, coherence, and phase spectra) were then compared for stationary parts of the data and the total data. This comparison indicated that nonstationarity affects all spectral measures. Most importantly, Stationarity x Task Condition x Frequency Band interactions were observed for coherence and phase spectra, and there were significant interactions with age for each of the spectral indices. These findings suggest that nonstationarity may result in biased outcomes of significance tests of the effects of task manipulations on the spectral indices of cardiac time series. Thus, it was concluded that the stationarity test should be routinely applied in the spectral analysis of physiological time series. In addition, it was suggested that the nonstationarity test has an even wider range of application that might be of interest to the psychophysiologist.     

The nonstationary strain filter in elastography: Part II. Lateral and elevational decorrelation

The nonstationary evolution of the strain filter due to lateral and elevational motion of the tissue scatterers across the ultrasound beam is analyzed for the 1-D cross-correlation-based strain estimator. The effective correlation coefficient that includes the contributions due to lateral and elevational signal decorrelation is used to derate the upper bound of the signal-to-noise ratio in the elastogram (SNR_e) predicted by the ideal strain filter. In the case of an elastically homogeneous target, if the transducer is on the axis of symmetry of such target in the elevational direction, the motion of the scatterers out the imaging plane is minimized. In addition, the ultrasound beam along the elevational direction is broader, allowing scatterers to stay longer within the beam during tissue compression. Under these conditions, lateral signal decorrelation becomes the primary contributor to the nonstationary behavior of the strain filter. Both the elastographic SNR_e and the dynamic range are reduced, with an increase in lateral decorrelation. Finite element simulations and phantom experiments are presented in this paper to corroborate the theoretical strain filter. The nonstationary behavior of the strain filter is reduced by confining the tissue in the lateral direction (minimizing motion of tissue scatterers), thereby improving the quality of the elastogram.     

Spatial and orientational heterogeneity in the statistical sensitivity of skeleton-based analyses of diffusion tensor MR imaging data

Group comparisons of indices derived from diffusion tensor imaging are common in the literature. An increasingly popular approach to performing such comparisons is the skeleton-projection based approach where, for example, fractional anisotropy (FA) values are projected onto a skeletonized version of the data to minimize differences due to spatial misalignment. In this work, we examine the spatial heterogeneity of the statistical power to detect group differences, and show that there is an intrinsic spatial heterogeneity, with more ‘central’ structures having less variance within a population. Importantly, we also demonstrate a previously unreported feature of skeleton-based analysis methods, that is that the width of the skeleton depends on the relative orientation to the imaging matrix. Due to the way in which the inferential statistics are performed, this means that structures that are obliquely oriented to the imaging matrix are more likely to show significant differences than when aligned with the imaging matrix. This has profound implications for the interpretation of results obtained from such analysis, especially when there are no a priori hypotheses concerning the spatial location of any group differences. For a uniform (DC) offset between two groups, the skeleton projection-based approaches will be most likely to reveal a difference in centrally located white matter structures oriented obliquely to the imaging matrix.     

Change-point detection method for clinical decision support system rule monitoring

A clinical decision support system (CDSS) helps clinicians to manage patients, but malfunctions of its components or other systems on which it depends may affect its intended functions. Monitoring the system and detecting changes in its behavior that may indicate the malfunction can help to avoid any potential costs associated with its improper operation. In this paper, we investigate the problem of detecting changes in the CDSS operation, in particular its monitoring and alerting subsystem, by monitoring its rule firing counts. We aim to screen and detect changes in real-time, that is whenever a new datum (rule firing count) arrives, we want to have a score indicating how likely there is a change in the system. We develop a new method based on Seasonal-Trend decomposition with locally weighted regression (Loess) and likelihood ratio statistics to detect the changes. Experiments on daily rule-firing-count data collected from a real CDSS and known change-points show that our method improves the detection performance when compared with existing change-point detection methods.     

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We define a novel feature, Normalized Vector Separation (γ _ij ), to measure the separation of two arbitrary states “i” and “j” in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that γ _ij can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via γ _ij , with small NNs having no more than 21 connection weight altogether.     

Early detection of epileptic seizures based on parameter identification of neural mass model

Physiologically based models are attractive for seizure detection, as their parameters can be explicitly related to neurological mechanisms. We propose an early seizure detection algorithm based on parameter identification of a neural mass model. The occurrence of a seizure is detected by analysing the time shift of key model parameters. The algorithm was evaluated against the manual scoring of a human expert on intracranial EEG samples from 16 patients suffering from different types of epilepsy. Results suggest that the algorithm is best suited for patients suffering from temporal lobe epilepsy (sensitivity was 95.0%±10.0% and false positive rate was 0.20±0.22 per hour).     

基于小波变换的心率变异性动态分析

心率变异性（Heart rate variability，HRV）分析已成为无创检测心脏自主神经调节功能的一种手段。传统的频域分析，主要是计算HRV信号各频段功率，以及识别各频段的峰值频率，无论是采用经典谱估计还是AR模型都是以假设HRV信号近似平稳为前提的。这种假设在短程分析中可以基本满足，但在长程分析中，HRV信号的非平稳性便凸现出来。提出了一种基于小波变换的心率变异性动态分析方法，它不但可以获得传统的频域指标，而且可以获得它们随时间变化的动态值，称为短时功率，短时LF／HF比，特别是后者，可以动态评估自主神经活动的平衡情况。最后将这种分析方法应用到阿托品药物实验中，跟踪分析了阿托品对自主神经的影响情况。     

Challenges for emerging neurostimulation-based therapies for real-time seizure control

In step with the worthwhile aim of this special issue, two junior investigators impart their insights on the therapeutic challenges imposed by pharmacoresistant epilepsies and offer viable approaches to improvement of treatment outcomes. Sunderam's comprehensive perspective addresses issues of critical importance for the design of efficacious therapies. Talathi delves into the thorny roles of so-called “interictal” spikes in ictio- and epileptogenesis, roles that are central to understanding the dynamics of these phenomena and implicitly of how to prevent them or abort them. First, however, Osorio and co-workers illustrate the complex behavior of the epileptogenic network and point to the importance of real-time intraindividual adaptation and optimization of therapies for seizures originating from the same epileptogenic network.