Noisy Series Research Articles

Horizontal visibility graphs: Exact results for random time series

The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape P(k)=(1/3)(2/3)(k-2), independent of the probability distribution from which the series was generated. Accordingly, visibility graphs with other P(k) are related to nonrandom series. Numerical simulations confirm the accuracy of the theorems for finite series. In a second part, we show that the method is able to distinguish chaotic series from independent and identically distributed (i.i.d.) theory, studying the following situations: (i) noise-free low-dimensional chaotic series, (ii) low-dimensional noisy chaotic series, even in the presence of large amounts of noise, and (iii) high-dimensional chaotic series (coupled map lattice), without needs for additional techniques such as surrogate data or noise reduction methods. Finally, heuristic arguments are given to explain the topological properties of chaotic series, and several sequences that are conjectured to be random are analyzed.

Complex network from time series based on phase space reconstruction

We propose in this paper a reliable method for constructing complex networks from a time series with each vector point of the reconstructed phase space represented by a single node and edge determined by the phase space distance. Through investigating an extensive range of network topology statistics, we find that the constructed network inherits the main properties of the time series in its structure. Specifically, periodic series and noisy series convert into regular networks and random networks, respectively, and networks generated from chaotic series typically exhibit small-world and scale-free features. Furthermore, we associate different aspects of the dynamics of the time series with the topological indices of the network and demonstrate how such statistics can be used to distinguish different dynamical regimes. Through analyzing the chaotic time series corrupted by measurement noise, we also indicate the good antinoise ability of our method.

Automatic stock decision support system based on box theory and SVM algorithm

The stock market is considered as a high complex and dynamic system with noisy, non-stationary and chaotic data series. So it is widely acknowledged that stock price series modeling and forecasting is a challenging work. A significant amount of work has been done in this field, and in them, soft computing techniques have showed good performance. Generally most of these works can be divided into two categories. One is to predict the future trend or price; another is to construct decision support system which can give certain buy/sell signals. In this paper, we propose a new intelligent trading system based on oscillation box prediction by combining stock box theory and support vector machine algorithm. The box theory believes a successful stock buying/selling generally occurs when the price effectively breaks out the original oscillation box into another new box. In the system, two SVM estimators are first utilized to make forecasts of the upper bound and lower bound of the price oscillation box. Then a trading strategy based on the two bound forecasts is constructed to make trading decisions. In the experiment, we test the system on different stock movement patterns, i.e. bull, bear and fluctuant market, and investigate the training of the system and the choice of the time span of the price box. The experiments on 442 S&P500 components show a promising performance is achieved and the system dramatically outperforms buy-and-hold strategy.

Order-crossing removal in Gabor order tracking by independent component analysis

Order-crossing problems in Gabor order tracking (GOT) of rotating machinery often occur when noise due to power–frequency interference, local structure resonance, etc., is prominent in applications. They can render the analysis results and the waveform-reconstruction tasks in GOT inaccurate or even meaningless. An approach is proposed in this paper to address the order-crossing problem by independent component analysis (ICA). With the approach, accurate order analysis results can be obtained and the waveforms of the order components of interest can be reconstructed or extracted from the recorded noisy data series. In addition, the ambiguities (permutation and scaling) of ICA results are also solved with the approach. The approach is amenable to applications in condition monitoring and fault diagnosis of rotating machinery. The evaluation of the approach is presented in detail based on simulations and an experiment on a rotor test rig. The results obtained using the proposed approach are compared with those obtained using the standard GOT. The comparison shows that the presented approach is more effective to solve order-crossing problems in GOT.

Computing the Light Periods of Blazars with the Periodogram Spectral Analysis Method

The periodogram spectral analysis method applicable to equallyspaced time series is discussed, and the method is tested first with a simulated data series. It is confirmed that this method is effective for noisy series. Then, applying this method to the analysis of the light periods of the quasars 3C 279 and 3C 345 as well as the BL Lac objects OJ 287 and ON 231, we obtain their light periods to be 7.14 yr, 10.00 yr, 11.76 yr and 6.80 yr, respectively. These results obtained by periodogram spectral analysis are consistent with those obtained by the Jurkevich method in the literature. We have analyzed the effects of different window functions, and commented on their correct selection in practical applications.

Detecting Trends in Noisy Data Series: Application to Biomarker Series

It is common to define a change in health status or in a disease state on the basis of a sustained rise (or decline) in a biomarker over time. However, such observations are often subject to important variability unrelated to the underlying biologic process. The authors propose a method to evaluate rules that define an event on the basis of consecutive increases (or decreases) in the observations, given the presence of random variation. They examine how well these rules correctly identify a truly rising biomarker trajectory and, conversely, how often they can recognize a truly stable series or a slowly rising series. The method relies on simulation of realistic, sophisticated data sets that accurately reflect the systematic and random variations observed in marker series. These flexible, empirically based simulations enable estimation of the sensitivity and specificity of rules of consecutive rises as a function of the underlying trend, amount of random variation, and schedule of measurements (frequency and duration of follow-up). The authors illustrate the approach with postradiotherapy series of prostate-specific antigen, where three consecutive rises in prostate-specific antigen indicate treatment failure; the data are described by using a Bayesian hierarchical changepoint model. The method is particularly flexible and could be applied to evaluate other rules that purport to accurately detect upturns (downturns) in other noisy data series, including other medical data or other application areas.

A generalized model for financial time series representation and prediction

Traditional financial analysis systems utilize low-level price data as their analytical basis. For example, a decision-making system for stock predictions regards raw price data as the training set for classifications or rule inductions. However, the financial market is a complex and dynamic system with noisy, non-stationary and chaotic data series. Raw price data are too random to characterize determinants in the market, preventing us from reliable predictions. On the other hand, high-level representation models which represent data on the basis of human knowledge of the problem domain can reduce the randomness in the raw data. In this paper, we present a high-level representation model easy to translate from low-level data into the machine representation. It is a generalized model in that it can accommodate multiple financial analytical techniques and intelligent trading systems. To demonstrate this, we further combine the representation with a probabilistic model for automatic stock trades and provide promising results.

Bootstrap nonlinear prediction

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy data series. In this paper, we proposed a scheme to effectively use near-neighbor information for more accurate estimation of the Jacobian matrix using the bootstrap resampling method. Then, to confirm the validity of the proposed method, we applied it to a mathematical model and several real time series. As a result, we confirmed that the proposed method greatly improves nonlinear predictability, not only for noise-corrupted mathematical models but also for real time series.

Performance of genetic programming to extract the trend in noisy data series

In this paper an approach based on genetic programming for forecasting stochastic time series is outlined. To obtain a suitable test-bed some well-known time series are dressed with noise. The GP approach is endowed with a multiobjective scheme relying on statistical properties of the faced series, i.e., on their momenta. Finally, the method is applied to the MIB30 Index series.

Atmospheric Angular Momentum Time-Series: Characterization of their Internal Noise and Creation of a Combined Series

The atmosphere induces variations in Earth rotation. These effects are classically computed using the “angular momentum approach”. In this method, the variations in Earth rotation are estimated from the variations in the atmospheric angular momentum (AAM). Several AAM time-series are available from different meteorological centers. However, the estimation of atmospheric effects on Earth rotation differs when using one atmospheric model or the other. The purpose of this work is to build an objective criterion that justifies the use of one series in particular. Because the atmosphere is not the only cause of Earth rotation variations, this criterion cannot rely only on a comparison of AAM series with geodetic data. Instead, we determine the quality of each series by making an estimation of their noise level, using a generalized formulation of the “three-cornered hat method”. We show the existence of a link between the noise of the AAM series and their correlation with geodetic data: a noisy series is usually less correlated with Earth orientation data. As the quality of the series varies in time, we construct a combined AAM series, using time-dependent weights chosen so that the noise level of the combined series is minimal. To determine the influence of a minimal noise level on the correlation with geodetic data, we compute the correlation between the combined series and Earth orientation data. We note that the combined series is always amongst the best correlated series, which confirms the link established before. The quality criterion, while totally independent of Earth orientation observations, appears to be physically convincing when atmospheric and geodetic data are compared

EFFECT OF NOISE ON THE AVERAGED FALSE NEIGHBORS METHOD APPLIED TO SIMULATED AND EXPERIMENTAL CHAOTIC TIMES SERIES

We examine the influence of noise on the averaged false neighbors method (AFN), which was proposed by L. Cao to identify the deterministic nature and estimate the minimum embedding dimension of time series. In a numerical experiment, we add a raising amount of noise to time series from numerical simulation of well known chaotic models and to experimentally recorded time series. We find that the AFN method acknowledges the deterministic nature of the underlying process of these noisy times series. For the assessment of the embedding, sensitivity to noise generally decreases when the dimension of the underlying dynamical process increased.

Digital processing of solid state detector signals in pellet charge exchange measurements on LHD

Radially resolved measurements of the plasma ion distribution function by detecting charge exchange neutrals from an impurity pellet ablation cloud require a fast operating energy analyzer working at high count rates to build several spectra during the pellet flight. Currently a solid state detector in the pulse height analysis (PHA) mode is used for such measurements on the Large Helical Device. Traditional PHA techniques cannot provide the operating speed required for a good spatial resolution. An algorithm has been proposed based on digital processing of noisy data series containing charge-sensitive preamplifier signals with discontinuities corresponding to incident particles. The algorithm employs the modified Tikhonov regularization and the successive detection–estimation of signal increments at discontinuity points. Such an approach allows one to realize an ultrafast particle energy spectroscopy by taking advantage of detector/preamplifier capabilities without limiting the system throughput by subsequent electronics.

Forecasting with computer-evolved model specifications: a genetic programming application

This paper uses genetic programming (GP) to evolve model specifications of time series data. GP is a computerized random search optimization algorithm that assembles equations until it identifies the fittest one. The technique is applied here to artificially simulated data first then to real-world sunspot numbers. One-step-ahead forecasts produced by the fittest of computer-evolved models are evaluated and compared with alternatives. The results suggest that GP may produce reasonable forecasts if their user selects appropriate input variables and comprehends the process investigated. Further, the technique appears promising in forecasting noisy complex series perhaps better than other existing methods. It is suitable for decision makers who set high priority on obtaining accurate forecasts rather than on probing into and approximating the underlying data generating process. Scope and purpose This paper contains a brief introduction and an evaluation of the use of genetic programming (GP) in forecasting time series. GP is a computerized random search optimization technique based upon Darwin's theory of evolution. The algorithm is first applied to model and forecast artificially simulated linear and nonlinear time series. Results are used to evaluate the effectiveness of GP as a forecasting technique. It is then applied to model and forecast sunspot numbers—the most frequently analyzed and forecasted series. An autoregressive and a threshold nonlinear dynamical systems to capture the dynamics of the irregular sunspot numbers’ cycle were tested using GP. The latter delivered estimated equations yielding the lowest mean square error ever reported for the series. This paper demonstrates that GP's forecasting capabilities depend on the structure and complexity of the process to model. Skills and intuition of GP's user are its limitation.

Application of computational mechanics to the analysis of natural data: An example in geomagnetism

We discuss how the ideal formalism of computational mechanics can be adapted to apply to a noninfinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that removes the corruption that creates rare unphysical causal states is demonstrated, and the concept of effective soficity is introduced. We believe that computational mechanics cannot be applied to a noisy and finite data series without invoking an argument based upon effective soficity. A related distinction between noise and unresolved structure is also defined: Noise can only be eliminated by increasing the length of the time series, whereas the resolution of previously unresolved structure only requires the finite memory of the analysis to be increased. The benefits of these concepts are demonstrated in a simulated times series by (a) the effective elimination of white noise corruption from a periodic signal using the expletive filter and (b) the appearance of an effectively sofic region in the statistical complexity of a biased Poisson switch time series that is insensitive to changes in the word length (memory) used in the analysis. The new algorithm is then applied to an analysis of a real geomagnetic time series measured at Halley, Antarctica. Two principal components in the structure are detected that are interpreted as the diurnal variation due to the rotation of the Earth-based station under an electrical current pattern that is fixed with respect to the Sun-Earth axis and the random occurrence of a signature likely to be that of the magnetic substorm. In conclusion, some useful terminology for the discussion of model construction in general is introduced.

1/f noise in pentacene and poly-thienylene vinylene thin film transistors

We investigate low frequency conductivity noise in the drain-source channel of organic material field-effect transistors by measuring the spectra of current fluctuations for several values of the gate voltage Vgs and drain voltage Vds and find that it is 1/f. The samples are biased in the ohmic range of the applied Vds. The relative current 1/f noise is inversely proportional to the charge carrier numbers N generated by illumination or by varying the gate-source voltage. Hooge’s empirical relation for the 1/f noise is validated for these organic semiconductors with an α≅0.01 for poly-thienylene vinylene and about 100 for pentacene thin film transistors. From geometry dependence of the noise we conclude that series resistance can be ignored for poly-thienylene vinylene field-effect transistors. However, some pentacene samples suffer from a noisy series resistance to the channel resistance. From the 1/f noise dependence on geometry and gate voltage bias we conclude that it can be used as a diagnostic tool for device quality assessment.

New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation

In this paper, we propose a novel method to assess standard errors and confidence intervals for the maximal Lyapunov exponent estimated on time continuous chaotic systems. The method is based on resampling the original series by means of spline interpolation in the time domain. In such a way, new time series of increased size are obtained, and the sample distribution of the estimators is constructed. The method is explained and tested on the basis of computer simulations both for clean and noisy series. We give evidence that the distribution of the maximal Lyapunov exponent calculated by this method fairly agrees with the one obtained by true series with different initial conditions. An empirical criterion for the choice of the parameters of the resampling is also suggested .

A Concordance Method For Analyzing Categorical Time Series. An Application For The Search of Periodicities

A simple method for searching for periods in biological series is proposed. Because it is based on an auto-comparison of the observations within a series we call it the concordance method. It requires few theoritical assumptions. In fact, even the ever present stationarity condition is not used. The method is compared with competing methods based on the khi-square periodogram. It is shown that the concordance method is much better for analyzing multimodal and noisy series. Rhythms presenting simultaneously circadian and ultradian components can also be analyzed with this method.

Detecting a global warming signal in hemispheric temperature series : A structural time series analysis

Non-stationary time series such as global and hemispheric temperatures, greenhouse gas concentrations, solar irradiance, and anthropogenic sulfate aerosols, may contain stochastic trends (the simplest stochastic trend is a random walk) which, due to their unique patterns, can act as a signal of the influence of other variables on the series in question. Two or more series may share a common stochastic trend, which indicates that either one series causes the behavior of the other or that there is a common driving variable. Recent developments in econometrics allow analysts to detect and classify such trends and analyze relationships among series that contain stochastic trends. We apply some univariate autoregression based tests to evaluate the presence of stochastic trends in several time series for temperature and radiative forcing. The temperature and radiative forcing series are found to be of different orders of integration which would cast doubt on the anthropogenic global warming hypothesis. However, these tests can suffer from size distortions when applied to noisy series such as hemispheric temperatures. We, therefore, use multivariate structural time series techniques to decompose Northern and Southern Hemisphere temperatures into stochastic trends and autoregressive noise processes. These results show that there are two independent stochastic trends in the data. We investigate the possible origins of these trends using a regression method. Radiative forcing due to greenhouse gases and solar irradiance can largely explain the common trend. The second trend, which represents the non-scalar non-stationary differences between the hemispheres, reflects radiative forcing due to tropospheric sulfate aerosols. We find similar results when we use the same techniques to analyze temperature data generated by the Hadley Centre GCM SUL experiment.

The CLEAN method of spectral analysis and its application to the oscillations of the cataclysmic variable TT Arietis

We studied the one-dimensional spectral analysis CLEAN applied to time series with unequal intervals, tested it with simulated signal, and showed it to be also applicable to noisy series, only the quality of the spectrum is closely correlated with the noise intensity. Applying this method to photometric data of the cataclysmic variable TT Ari quasi-periodic oscillations with periods around 20 min are recovered.

Analytical behavior of the noise resistance and the noise conductance for a network with parallel and series feedback

An analysis is presented of the changes of the noise parameters of a two-port network when noisy series and parallel feedback immittances are applied. Exact formulas for the noise parameters R/sub n/, g/sub n/, and /spl rho//sub n/ are given as functions of the feedback for a given network. It is proved that R/sub n/ always reaches a minimum when a reactive series feedback is considered. The same results are demonstrated for g/sub n/ since a duality principle is pointed out. The results are valid for a wide range of linear microwave two-port networks, either passive or active, and they are used to confirm the data from previously published work.