Analysis Of Discrete Time Series Research Articles

A Tool to Explore Discrete-Time Data: The Time Series Response Analyser.

The analysis of time series data is common in nutrition and metabolism research for quantifying the physiological responses to various stimuli. The reduction of many data from a time series into a summary statistic(s) can help quantify and communicate the overall response in a more straightforward way and in line with a specific hypothesis. Nevertheless, many summary statistics have been selected by various researchers, and some approaches are still complex. The time-intensive nature of such calculations can be a burden for especially large data sets and may, therefore, introduce computational errors, which are difficult to recognize and correct. In this short commentary, the authors introduce a newly developed tool that automates many of the processes commonly used by researchers for discrete time series analysis, with particular emphasis on how the tool may be implemented within nutrition and exercise science research.

Fractal Lifting Wavelets for Machine Fault Diagnosis

Fault diagnosis is of vital importance in safety and reliable operations of modern electromechanical systems. Advanced signal processing techniques are indispensable for extracting incipient features from measured dynamical signals. For discrete wavelet analysis, shift-invariance and proper frequency-scale configuration are both necessary for effective investigation of incipient fault features. In this paper, a novel fractal lifting scheme is proposed based on redundant second generation wavelet packet decomposition (RSGWPD). Implicit wavelet packets (IWPs), generated via fractal lifting scheme, can realize a novel centralized multiresolution. It is demonstrated that each IWP inherits the property of exact shift-invariance originated from redundant lifting scheme. In addition, a novel concept of nested centralized wavelet packet cluster is introduced for explaining merits provided by sets composed of IWPs. The numerical simulations were employed to validate the benefits of exact shift-invariance in a multiscale analysis of discrete time series. RSGWPD and IWPs are combined to conduct multiscale expansion of vibration measurement. To further explore optimal features, an indicator of spatial-spectral ensemble kurtosis is utilized to select optimal analysis parameters. The proposed technique was successfully applied to case studies of gearbox fault diagnosis as well as bearing fault diagnosis. The comparisons were made between results by the proposed technique and those provided by some other mainstream adaptive signal decomposition methodologies. It is verified that the combination of exact shift-invariance and centralized multiresolution significantly enhances the performance of incipient fault feature extraction of nonstationary vibration signals.

Measure of regularity in discrete time signals

Discrete time series can be treated through linear or non-linear mathematical procedures in order to find specific properties. Last decades, non-linear analysis methods brought valuable results in discrete time series analysis and prediction. Statistical signal processing methods as entropy measures have become important tools in the analysis of time series data, especially in physiology and medicine. Generally, entropy measures the degree of regularity in systems and usually it should be able to quantify the complexity of any underlying structure in the discrete time signals. This paper proposes approximate entropy and sample entropy calculations on synthesized test signals with specific properties in order to try to find hidden properties. Approximate entropy and sample entropy being mathematical algorithms created to measure the regularity or predictability within a time series, are extremely sensitive to their used parameters as length of the data segment and length of data.

Numerical estimates of the adequacy of a mathematical model of hydroelastic oscillations in curved pipelines

The problem was set in the research context of water hammer in the pipeline system with complex configuration. Usually, the experimental data in the literature on such pipelines are limited to the charts of the unknown functions. Numerical criteria of the adequacy of a mathematical model for a pipeline and an algorithm for its quantitative verification are selected for the case where data is presented in a reference source only by the charts of functions. A new mathematical model is presented and a series of numerical experiments for the water hammer in a variety of curved pipelines have been performed. To verify the model, two pipelines are taken: a pipeline consisting of seven sections of the total length of 48 m, and a smoothly curved pipe of the total length of 624 mm. In addition, acoustic oscillations of a bent pipe of 300 mm in length are calculated. Based on the published data on these pipelines and the results of numerical experiments, quantitative characteristics of the adequacy of the mathematical model proposed are found. These characteristics are the results from statistical analysis of discrete time series of fluid pressure, which are obtained by digitizing charts from the articles referenced here and by solving equations of the tested model. It has been found that the description of the results of field experiments by the proposed mathematical model exhibits accuracy close to that of a mathematical description of the reference sources. In the case when a pipe consists of seven sections, its accuracy can be improved using the parameter identification methods. Thus, the proposed mathematical model adequately describes the results obtained for hydraulic shock in pipes and covers different cases of hydro-elastic vibrations from a unified viewpoint.

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.

Neural coding tools, based on Information Theory, applied to discrete time series: from electrophysiology to neuroethology

We developed a method based on Information Theory [1] to the analysis of discrete time series applied to spike and pulse sequences in two different systems: Central Pattern Generator (CPG) motor neurons in the crustacean stomatogastric ganglion (biological and model neurons) and electrocommunication in weakly electric fish interacting with an artificial fish. CPG motor neurons [4][5] in the nervous systems are responsible for the mechanical digestion flow of fluids from the stomach to the intestines. They present an extensive dynamic repertoire due to a large variety of ion channels and modulation mechanisms. The rhythm and the average discharge frequency of these neurons must be constant to ensure a proper muscular contraction, nevertheless there are patterns associated to a very detailed inter spike distributions in which muscular contraction do not take part [3]. What are these patterns for? Experiments were performed in a pair of pyloric CPG neurons with simultaneously intracellular recordings, both in control condition (intact CPG) and with a hybrid network where one neuron was replaced by a computational model (real time interface). Information theoretical analysis showed that a motor neuron is able to express information encoded in spike intervals (ISIs) from another one (both biological and artificial neuron) in a very fine time scale. Weakly electric fish provide a wonderful opportunity to study and interact with a living intact nervous systems. Their electrical organ discharges (EODs) are not only complex signals that belong to the processing of environmental sensory information by the nervous system but they are also easy-to-detect. Each EOD generates an electric field that reaches a myriad of electroreceptors disposed to detect small changes in the cutaneous electric field. With this apparatus the weakly electric fishes are able to detect objects as well as social electrocommunication[2]. Using non invasive techniques in a freely moving fish we were able to record its organ electric discharges (EODs) for long periods (~ hours). Electrocommunication experiments were performed, in which electric stimuli sequences, mimicking the fish EODs, were sent to a measurement tank via artificial fish, both in real time and previously recorded sequences. Analysis using Information Theory tools revealed that the stimuli sequences play a significant role in the fish response.

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.

Stability properties for generalized fractional differential systems

In the last decades, fractional differential equations have become popular among scientists in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the autocorrelation of which also exhibits an anomalous decay. Both types of models stem from a common property of complex variable functions: namely, multivalued functions and their behaviour in the neighborhood of the branching point, and asymptotic expansions performed along the cut between branching points. This more abstract point of view proves very much useful in order to extend these models by changing the location of the classical branching points (the origin of the complex plane, for continuous-time systems). Hence, stability properties of and modelling issues by generalized fractional differential systems will be adressed in the present paper: systems will be considered both in the time-domain and in the frequency-domain; when necessary a distinction will be made between fractional differential systems of commensurate and incommensurate.

DHugin: a computational system for dynamic time-sliced Bayesian networks

A computational system for reasoning about dynamic time-sliced systems using Bayesian networks is presented. The system, called dHugin, may be viewed as a generalization of the inference methods of classical discrete time-series analysis in the sense that it allows description of non-linear, discrete multivariate dynamic systems with complex conditional independence structures. The paper introduces the notions of dynamic time-sliced Bayesian networks, a dynamic time window, and common operations on the time window. Inference, pertaining to the time window and time slices preceding it, are formulated in terms of the well-known message passing scheme in junction trees. Backward smoothing, for example, is performed efficiently through inter-tree message passing. Further, the system provides an efficient Monte-Carlo algorithm for forecasting; i.e. inference pertaining to time slices succeeding the time window. The system has been implemented on top of the Hugin shell.

Identification of a Mechanistic Model for the Diurnal Dissolved Oxygen Pattern in Lakes with Discrete Time Series Analysis

Discrete time data analysis indicates that a first-order autoregressive model with exogenous variables (ARX) is sufficient to describe observed diurnal dissolved oxygen patterns in a lake. It is shown that this model is equivalent to a simple three parameter mechanistic model, augmented with a first-order noise filter. The noise dynamics can be interpreted in terms of natural stochastic parameter variations. Tests with data simulated with the identified stochastic model structure reveal that the usual least squares (LSQ) fitting of the mechanistic model without the noise term leads to biased parameter estimates. Therefore, with the actually measured data, ARX parameter estimates are probably preferable to LSQ estimates, even though the output error is larger. In the true system slow parameter variations probably also occur which are not covered by the simple model.

Spectrum analysis—A modern perspective

A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.