Discrete Time Series Research Articles

Statistical Anomaly Detection for Individuals With Cognitive Impairments

We study anomaly detection in a context that considers user trajectories as input and tries to identify anomalies for users following normal routes such as taking public transportation from the workplace to home or vice versa. Trajectories are modeled as a discrete-time series of axis-parallel constraints ("boxes") in the 2-D space. The anomaly can be estimated by considering two trajectories, where one trajectory is the current movement pattern and the other is a weighted trajectory collected from N norms. The proposed system was implemented and evaluated with eight individuals with cognitive impairments. The experimental results showed that recall was 95.0% and precision was 90.9% on average without false alarm suppression. False alarms and false negatives dropped when axis rotation was applied. The precision with axis rotation was 97.6% and the recall was 98.8%. The average time used for sending locations, running anomaly detection, and issuing warnings was in the range of 15.1-22.7s. Our findings suggest that the ability to adapt anomaly detection devices for appropriate timing of self-alerts will be particularly important.

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series

We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ~3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.

VO2 and VCO2 variabilities through indirect calorimetry instrumentation

The aim of this paper is to understand how to measure the VO2 and VCO2 variabilities in indirect calorimetry (IC) since we believe they can explain the high variation in the resting energy expenditure (REE) estimation. We propose that variabilities should be separately measured from the VO2 and VCO2 averages to understand technological differences among metabolic monitors when they estimate the REE. To prove this hypothesis the mixing chamber (MC) and the breath-by-breath (BbB) techniques measured the VO2 and VCO2 averages and their variabilities. Variances and power spectrum energies in the 0–0.5 Hertz band were measured to establish technique differences in steady and non-steady state. A hybrid calorimeter with both IC techniques studied a population of 15 volunteers that underwent the clino-orthostatic maneuver in order to produce the two physiological stages. The results showed that inter-individual VO2 and VCO2 variabilities measured as variances were negligible using the MC while variabilities measured as spectral energies using the BbB underwent 71 and 56% (p < 0.05), increase respectively. Additionally, the energy analysis showed an unexpected cyclic rhythm at 0.025 Hertz only during the orthostatic stage, which is new physiological information, not reported previusly. The VO2 and VCO2 inter-individual averages increased to 63 and 39% by the MC (p < 0.05) and 32 and 40% using the BbB (p < 0.1), respectively, without noticeable statistical differences among techniques. The conclusions are: (a) metabolic monitors should simultaneously include the MC and the BbB techniques to correctly interpret the steady or non-steady state variabilities effect in the REE estimation, (b) the MC is the appropriate technique to compute averages since it behaves as a low-pass filter that minimizes variances, (c) the BbB is the ideal technique to measure the variabilities since it can work as a high-pass filter to generate discrete time series able to accomplish spectral analysis, and (d) the new physiological information in the VO2 and VCO2 variabilities can help to understand why metabolic monitors with dissimilar IC techniques give different results in the REE estimation.

Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

Sampling of a continuous flow in the plane based on two-dimensional variogram models

Theory of sampling from one-dimensional continuous material flows is well established in developments following the original path breaking work by P. Gy, based on an extensively employed tool named variogram and its modelling. These developments could be regarded as a continuous analogue of the discrete time series approach in one dimensional sampling due to W. G. Cochran, whose work was further unified with the variogram approach by G.H. Jowett. Extension of Cochran’s discrete time series approach to plane sampling, from equally spaced grid locations in two dimensions, was carried out, independently, by M. H. Quenouille and R. Das. Gy’s development is an off-shoot of a closely related geostatistical theory, pioneered by G. Matheron, for collecting and analysing data in three dimensional space. Geostatistical approach generally employed a variogram based on a Euclidean distance to provide a three dimensional modelling of spatial variation structures. Most of the successful variogram modelling approach is essentially based on geometrically isotropic one-dimensional variogram models, instead of variogram models based on generalised distance functions or distance functions in separate dimensions. Quenouille explicitly proposed a geometrically anisotropic two-dimensional autocorrelation function which could be readily reparameterised to obtain a two-dimensional elliptical variogram. Both plane sampling approach and geostatistical approach provide techniques of assessing the uncertainty of the sample average as an estimate of the overall population mean, by the respective techniques of two-dimensional discrete sampling and spatial variogram modelling. The present paper (i) outlines the connection between the precision formula based on plane sampling approach and that based on traditional geostatistical approach, via a unified framework in which the two methods can be compared on an equal footing, with or without equal spacing along the X-direction and/or the Y-direction (ii) proposes an elliptical empirical variogram model, as a two-dimensional exponential type variogram, obtained as a re-parameterised version of Quenouille’s elliptical auto-correlation function and (iii) provides a computationally robust algorithm for fitting a two-dimensional elliptical variogram model to an observed variogram in two dimensions by an approximate likelihood method, in addition to a demonstration of the developed methodology to a data set, available in the published literature.

Numerical Research on Self-Sustained Oscillation and Chaos of Natural Convection in Horizontal Fluids Layer

Numerical simulation was conducted to study self-sustained oscillation and chaos of natural convection in horizontal fluids layer heated from below. The numerical simulation was conducted using SIMPLE algorithm with a QUICK scheme. Discrete time series was analyzed to study stability problem. Correlation dimension was calculated, their frequency characteristics were analyzed and chaos attractor was extracted. The results showed that oscillation appeared when Ra was over 2×104 and chaos appeared when Ra was over 5×106. When parameter was varied, chaos appeared. Strange attractor was used to describe chaos system. Fractal dimension of strange attractor was 1.19. Saturated embedding dimension of phase space reconstruction was 5. The time delay was selected for 5.

Memory and long-range correlations in chess games

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations; rescaled range analysis and detrended fluctuation analysis. We found that long-range memory is related to the level of the players. When the database is filtered according to player levels we found differences in the persistence of the different subsets. For high level players, correlations are stronger at long time scales; whereas in intermediate and low level players they reach the maximum value at shorter time scales. This can be interpreted as a signature of the different strategies used by players with different levels of expertise. These results are robust against the assignation rules and the method employed in the analysis of the time series.

The Research of Chaos Time Series on Chatter Signal Recognition

The online detecting of chatter is the key technology to improve the machining quality. Based on the nonlinear chaos control theory in discrete dynamic system, the processing vibration signal discrete time series is taken as system nonlinear input, the C-C algorithm and correlation integral was used to determine appropriate embedding dim m and time delay τ. Then the phase space is reconstructed by discrete vibration signal. In milling chatters experiment, the time series analysis method is used to get the phase diagram before and after chatter. The chatter phase chart shows the characteristics of chaos and recognized the milling chatter.

Online Monitoring Recognition Theory Based on the Time Series of Chatter

On-line monitoring recognition for machining chatter is one of the key technologies in manufacturing. Based on the nonlinear chaotic control theory, the vibration signal discrete time series for on-line monitoring indicator is studed. As in chatter the chaotic dynamics process attractor dimension is reduced, the KolmogorovSinai entropy (K-S) index is extracted to reflected the regularity of workpiece chatter, then the k-S entropy is simplified by coarse - grained entropy rate (CER), which can easily evaluated as chatter online monitoring threshold value. The milling test shows that the CER have a sharp decline when chatter occurre, and can quickly and accurately forecast chatter.

NONPARAMETRIC NONSTATIONARITY TESTS

We propose additive functional-based nonstationarity tests that exploit the different divergence rates of the occupation times of a (possibly nonlinear) process under the null of nonstationarity (stationarity) versus the alternative of stationarity (nonstationarity). We consider both discrete-time series and continuous-time processes. The discrete-time case covers Harris recurrent Markov chains and integrated processes. The continuous-time case focuses on Harris recurrent diffusion processes. Notwithstanding finite-sample adjustments discussed in the paper, the proposed tests are simple to implement and rely on tabulated critical values. Simulations show that their size and power properties are satisfactory. Our robustness to nonlinear dynamics provides a solution to the typical inconsistency problem between assumed linearity of a time series for the purpose of nonstationarity testing and subsequent nonlinear inference.

Some properties of multivariate INAR(1) processes

INteger-valued AutoRegressive (INAR) processes are common choices for modeling non-negative discrete valued time series. In this framework and motivated by the frequent occurrence of multivariate count time series data in several different disciplines, a generalized specification of the bivariate INAR(1) (BINAR(1)) model is considered. In this new, full BINAR(1) process, dependence between the two series stems from two sources simultaneously. The main focus is on the specific parametric case that arises under the assumption of a bivariate Poisson distribution for the innovations of the process. As it is shown, such an assumption gives rise to a Hermite BINAR(1) process. The method of conditional maximum likelihood is suggested for the estimation of its unknown parameters. A short application on financial count data illustrates the model.

Spectral fluctuation and correlation structure ofδnstatistics in the spectra of interacting trapped bosons

It is a well-known fact that the statistical behaviors of level fluctuation and level correlation in the energy-level spectra are the most efficient tool to characterize quantum chaos in nonintegrable quantum systems. The system of interacting trapped bosons is a complex system where the low-lying energy levels are highly influenced by the level repulsion. In this case, interatomic interaction is a dominating fact with strong level correlation between distant levels. Here we numerically calculate the correlation function, number variance, and Dyson-Mehta least-square deviation for the low-lying levels for a few thousand interacting trapped bosons, and our data show good analogy with the Gaussian orthogonal ensemble (GOE) results with a signature of chaos. In the next part of our study, the energy spectrum of these low-lying levels is considered as a discrete signal and the fluctuation of the excitation energy is considered as discrete time series. Then we calculate numerically the height-height correlation function for different order of momentum. In our study logarithmic correlation structure is found instead of multiscaling structure, and we observe that spectral statistics are compatible with those of GOE.

Adaptively combined forecasting for discrete response time series

Adaptive combining is generally a desirable approach for forecasting, which, however, has rarely been explored for discrete response time series. In this paper, we propose an adaptively combined forecasting method for such discrete response data. We demonstrate in theory that the proposed forecast is of the desired adaptation with respect to the widely used squared risk and other significant risk functions under mild conditions. Furthermore, we study the issue of adaptation for the proposed forecasting method in the presence of model screening that is often useful in applications. Our simulation study and two real-world data examples show promise for the proposed approach.

On Estimation of the Bivariate Poisson INAR Process

In a recent article, Pedeli and Karlis (2010) examined the extension of the classical Integer–valued Autoregressive (INAR) model to the bivariate case. In the present article, we examine estimation methods for the case of bivariate Poisson innovations. This is a simple extension of the classical INAR model allowing for two discrete valued time series to be correlated. Properties of different estimators are given. We also compare their properties via a small simulation experiment. Extensions to incorporate covariate information is discussed. A real data application is also provided.

Cluster analysis of WIBS single-particle bioaerosol data

Abstract. Hierarchical agglomerative cluster analysis was performed on single-particle multi-spatial data sets comprising optical diameter, asymmetry and three different fluorescence measurements, gathered using two dual Wideband Integrated Bioaerosol Sensors (WIBSs). The technique is demonstrated on measurements of various fluorescent and non-fluorescent polystyrene latex spheres (PSL) before being applied to two separate contemporaneous ambient WIBS data sets recorded in a forest site in Colorado, USA, as part of the BEACHON-RoMBAS project. Cluster analysis results between both data sets are consistent. Clusters are tentatively interpreted by comparison of concentration time series and cluster average measurement values to the published literature (of which there is a paucity) to represent the following: non-fluorescent accumulation mode aerosol; bacterial agglomerates; and fungal spores. To our knowledge, this is the first time cluster analysis has been applied to long-term online primary biological aerosol particle (PBAP) measurements. The novel application of this clustering technique provides a means for routinely reducing WIBS data to discrete concentration time series which are more easily interpretable, without the need for any a priori assumptions concerning the expected aerosol types. It can reduce the level of subjectivity compared to the more standard analysis approaches, which are typically performed by simple inspection of various ensemble data products. It also has the advantage of potentially resolving less populous or subtly different particle types. This technique is likely to become more robust in the future as fluorescence-based aerosol instrumentation measurement precision, dynamic range and the number of available metrics are improved.

A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series

Statistical analysis and synthesis of self-similar discrete time signals are presented. The analysis equation is formally defined through a special family of basis functions of which the simplest case matches the Haar wavelet. The original discrete time series is synthesized without loss by a linear combination of the basis functions after some scaling, displacement, and phase shift. The decomposition is then used to synthesize a new second-order self-similar signal with a different Hurst index than the original. The components are also used to describe the behavior of the estimated mean and variance of self-similar discrete time series. It is shown that the sample mean, although it is unbiased, provides less information about the process mean as its Hurst index is higher. It is also demonstrated that the classical variance estimator is biased and that the widely accepted aggregated variance-based estimator of the Hurst index results biased not due to its nature (which is being unbiased and has minimal variance) but to flaws in its implementation. Using the proposed decomposition, the correct estimation of theVariance Plotis described, as well as its close association with the popularLogscale Diagram.

Predictive Likelihood Comparisons with DSGE and DSGE-VAR Models

This paper shows how to compute the h-step-ahead predictive likelihood for any subset of the observed variables in parametric discrete time series models estimated with Bayesian methods. The subset of variables may vary across forecast horizons and the problem thereby covers marginal and joint predictive likelihoods for a fixed subset as special cases. The basic idea is to utilize well-known techniques for handling missing data when computing the likelihood function, such as a missing observations consistent Kalman filter for linear Gaussian models, but it also extends to nonlinear, nonnormal state-space models. The predictive likelihood can thereafter be calculated via Monte Carlo integration using draws from the posterior distribution. As an empirical illustration, we use euro area data and compare the forecasting performance of the New Area-Wide Model, a small-open-economy DSGE model, to DSGEVARs, and to reduced-form linear Gaussian models. JEL Classification: C11, C32, C52, C53, E37

Estimating Coastal Lagoon Tidal Flooding and Repletion with Multidate ASTER Thermal Imagery

Coastal lagoons mix inflowing freshwater and tidal marine waters in complex spatial patterns. This project sought to detect and measure temperature and spatial variability of flood tides for a constricted coastal lagoon using multitemporal remote sensing. Advanced Spaceborne Thermal Emission Radiometer (ASTER) thermal infrared data provided estimates of surface temperature for delineation of repletion zones in portions of Chincoteague Bay, Virginia. ASTER high spatial resolution sea-surface temperature imagery in conjunction with in situ observations and tidal predictions helped determine the optimal seasonal data for analyses. The selected time series ASTER satellite data sets were analyzed at different tidal phases and seasons in 2004–2006. Skin surface temperatures of ocean and estuarine waters were differentiated by flood tidal penetration and ebb flows. Spatially variable tidal flood penetration was evaluated using discrete seed-pixel area analysis and time series Principal Components Analysis. Results from these techniques provide spatial extent and variability dynamics of tidal repletion, flushing, and mixing, important factors in eutrophication assessment, water quality and resource monitoring, and application of hydrodynamic modeling for coastal estuary science and management.

Saccadic Reaction Times to Audiovisual Stimuli Show Effects of Oscillatory Phase Reset

Initiating an eye movement towards a suddenly appearing visual target is faster when an accessory auditory stimulus occurs in close spatiotemporal vicinity. Such facilitation of saccadic reaction time (SRT) is well-documented, but the exact neural mechanisms underlying the crossmodal effect remain to be elucidated. From EEG/MEG studies it has been hypothesized that coupled oscillatory activity in primary sensory cortices regulates multisensory processing. Specifically, it is assumed that the phase of an ongoing neural oscillation is shifted due to the occurrence of a sensory stimulus so that, across trials, phase values become highly consistent (phase reset). If one can identify the phase an oscillation is reset to, it is possible to predict when temporal windows of high and low excitability will occur. However, in behavioral experiments the pre-stimulus phase will be different on successive repetitions of the experimental trial, and average performance over many trials will show no signs of the modulation. Here we circumvent this problem by repeatedly presenting an auditory accessory stimulus followed by a visual target stimulus with a temporal delay varied in steps of 2 ms. Performing a discrete time series analysis on SRT as a function of the delay, we provide statistical evidence for the existence of distinct peak spectral components in the power spectrum. These frequencies, although varying across participants, fall within the beta and gamma range (20 to 40 Hz) of neural oscillatory activity observed in neurophysiological studies of multisensory integration. Some evidence for high-theta/alpha activity was found as well. Our results are consistent with the phase reset hypothesis and demonstrate that it is amenable to testing by purely psychophysical methods. Thus, any theory of multisensory processes that connects specific brain states with patterns of saccadic responses should be able to account for traces of oscillatory activity in observable behavior.

Sparse Contour Representations of Sound

Many signals are naturally described by continuous contours in the time-frequency plane, but standard time-frequency methods disassociate continuous structures into isolated “atoms” of energy. Here we propose a method that represents any discrete time-series as a set of time-frequency contours. The edges of the contours are defined by fixed points of a generalized reassignment algorithm. These edges are linked together by continuity such that each contour represents a single phase-coherent region of the time-frequency plane. By analyzing the signal across many time-scales, an over-complete set of contours is generated, and from this redundant set of shapes the simplest, most parsimonious forms may be selected. The result is an adaptive time-frequency analysis that can emphasize the continuity of long-range structure. The proposed method is demonstrated with a few examples.