TIME SERIES ANALYSIS OF COMPLEX DYNAMICAL BEHAVIOR CONTAMINATED WITH OBSERVATIONAL NOISE

1996 ◽  
Vol 06 (11) ◽  
pp. 2031-2045 ◽  
Author(s):  
TAKAYA MIYANO
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Random Noise ◽  
Dynamical Behavior ◽  
Deterministic Chaos ◽  
Diagnostic Algorithm ◽  
Diagnostic Methods ◽  
Observational Noise ◽  
Nonlinear Forecasting ◽  
Complex Dynamical Behavior

Diagnostic methods for discovering deterministic chaos based on the instability and the parallelness of nearby trajectories generated from a time series in phase space are applied to numerical time series contaminated with additive random noise. The diagnostic algorithm based on nonlinear forecasting is prone to be fooled when handling chaotic data including observational noise. Such a misdiagnosis can be circumvented by estimating the degrees of parallelness of neighboring trajectories in the phase space. Dynamical properties of global temperature variations and voice signals of Japanese vowel /a/ are examined by the combinational use of the diagnostic algorithms.

Chaos in blood flow control in genetic and renovascular hypertensive rats

1991 ◽  
Vol 261 (3) ◽  
pp. F400-F408 ◽  
Author(s):  
K. P. Yip ◽  
N. H. Holstein-Rathlou ◽  
D. J. Marsh
Keyword(s):  
Time Series ◽  
Blood Flow ◽  
Phase Space ◽  
Renal Artery ◽  
Initial Conditions ◽  
Pressure Fluctuations ◽  
Deterministic Chaos ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Statistical Measures

Hydrostatic pressure and flow in renal proximal tubules oscillate at 30–40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange attractor, and the largest Lyapunov exponent, a measure of the rate of divergence in phase space, was positive, indicating sensitivity to initial conditions. These time series therefore satisfy two criteria of deterministic chaos. The measures were the same in SHR as in rats with renovascular hypertension. Since two different models of hypertension displayed similar dynamics, we suggest that chaotic behavior is a common feature of renal vascular control in the natural history of the disease.

scholarly journals The Application of Random Noise Reduction By Nearest Neighbor Method To Forecasting of Economic Time Series

2014 ◽  
Vol 13 (2) ◽  
pp. 96-108
Author(s):  
Monika Miśkiewicz-Nawrocka
Keyword(s):  
Time Series ◽  
Nearest Neighbor ◽  
Financial Time Series ◽  
Random Noise ◽  
Time Series Prediction ◽  
Deterministic Chaos ◽  
Largest Lyapunov Exponent ◽  
Economic Time Series ◽  
Economic Time

Abstract Since the deterministic chaos appeared in the literature, we have observed a huge increase in interest in nonlinear dynamic systems theory among researchers, which has led to the creation of new methods of time series prediction, e.g. the largest Lyapunov exponent method and the nearest neighbor method. Real time series are usually disturbed by random noise, which can complicate the problem of forecasting of time series. Since the presence of noise in the data can significantly affect the quality of forecasts, the aim of the paper will be to evaluate the accuracy of predicting the time series filtered using the nearest neighbor method. The test will be conducted on the basis of selected financial time series.

Determinism Measurement in Time Series by Chaotic Approach and Its Applications

1999 ◽  
Vol 3 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Yasunari Fujimoto ◽  
◽  
Tadashi Iokibe
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Random Noise ◽  
Automatic Transmission ◽  
Deterministic Chaos ◽  
Chaotic Time Series ◽  
Practical Application ◽  
Characteristic Frequencies ◽  
Parallel Measurement ◽  
Continuous Power

Frequently irregular-looking time series may have a deterministic cause, which is why it is called deterministic chaos. Even if a time series has a little noise, it is not always easy to recognize noise by looking at data. Fast Fourier transform (FFT) is used to extract characteristic frequencies. A chaotic time series consists of an infinite number of frequency elements, producing a broad continuous power spectrum but has few distinguishable characteristics. We propose a way, called trajectory parallel measurement (TPM), based on the chaotic approach to distinguish determinism and randomness in a time series, and apply this to a chaotic time series with random noise, summarizing the results of practical application in diagnosing automatic transmission.

METHODS FOR QUANTIFYING THE CAUSAL STRUCTURE OF BIVARIATE TIME SERIES

2007 ◽  
Vol 17 (03) ◽  
pp. 903-921 ◽  
Author(s):  
M. LUNGARELLA ◽  
K. ISHIGURO ◽  
Y. KUNIYOSHI ◽  
N. OTSU
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Causal Structure ◽  
Dynamical Behavior ◽  
World Systems ◽  
Flow Of Information ◽  
Additional Constraints ◽  
Complex Dynamical Behavior ◽  
Bivariate Time Series

In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni- and bidirectionally coupled deterministic chaotic systems.

scholarly journals Non-linear analysis of geomagnetic time series from Etna volcano

2004 ◽  
Vol 11 (1) ◽  
pp. 119-125 ◽  
Author(s):  
G. Currenti ◽  
C. Del Negro ◽  
L. Fortuna ◽  
R. Napoli ◽  
A. Vicari
Keyword(s):  
Time Series ◽  
Dynamical Behavior ◽  
Predictive Ability ◽  
Prediction Errors ◽  
Etna Volcano ◽  
Short Term ◽  
Complex Processes ◽  
Nonlinear Forecasting ◽  
Low Dimensional ◽  
Magnetic Network

Abstract. An intensive nonlinear analysis of geomagnetic time series from the magnetic network on Etna volcano was carried out to investigate the dynamical behavior of magnetic anomalies in volcanic areas. The short-term predictability of the geomagnetic time series was evaluated to establish a possible low-dimensional deterministic dynamics. We estimated the predictive ability of both a nonlinear forecasting technique and a global autoregressive model by comparing the prediction errors. Our findings highlight that volcanomagnetic signals are the result of complex processes that cannot easily be predicted. There is slight evidence based on nonlinear predictions, that the geomagnetic time series are to be governed by many variables, whose time evolution could be better regarded as arising from complex high dimensional processes.

scholarly journals Electrochemical Noise Chaotic Analysis of NiCoAg Alloy in Hank Solution

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
D. Bahena ◽  
I. Rosales ◽  
O. Sarmiento ◽  
R. Guardián ◽  
C. Menchaca ◽  
...  
Keyword(s):  
Time Series ◽  
Electrochemical Impedance ◽  
Random Noise ◽  
Deterministic Chaos ◽  
Fractal Dimensions ◽  
Corrosion Mechanism ◽  
Power Spectral ◽  
Fractal Analyses ◽  
Power Spectral Densities ◽  
Hank Solution

The potential and current oscillations during corrosion of NiCoAg alloy in Hank solution were studied. Detailed nonlinear fractal analyses were used to characterize complex time series clearly showing that the irregularity in these time series corresponds to deterministic chaos rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space, and Lyapunov exponents. Electrochemical impedance was also applied the fractal dimensions for the corroded surface was obtained, and a corrosion mechanism was proposed.

Time series analysis and prediction on complex dynamical behavior observed in a blast furnace

2000 ◽  
Vol 135 (3-4) ◽  
pp. 305-330 ◽  
Author(s):  
T. Miyano ◽  
S. Kimoto ◽  
H. Shibuta ◽  
K. Nakashima ◽  
Y. Ikenaga ◽  
...  
Keyword(s):  
Time Series ◽  
Blast Furnace ◽  
Time Series Analysis ◽  
Dynamical Behavior ◽  
Series Analysis ◽  
Complex Dynamical Behavior

Nonlinear forecasting for the classification of natural time series

1994 ◽  
Vol 348 (1688) ◽  
pp. 477-495 ◽  
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Classification Problems ◽  
Ecological Data ◽  
Dynamic Complexity ◽  
Natural Time ◽  
Good Discriminator ◽  
Observational Noise ◽  
Nonlinear Forecasting ◽  
Short Time

There is a growing trend in the natural sciences to view time series as products of dynamical systems. This viewpoint has proven to be particularly useful in stimulating debate and insight into the nature of the underlying generating mechanisms. Here I review some of the issues concerning the use of forecasting in the detection of nonlinearities and possible chaos, particularly with regard to stochastic chaos. Moreover, it is shown how recent attempts to measure meaningful Lyapunov exponents for ecological data are fundamentally flawed, and that when observational noise is convolved with process noise, computing Lyapunov exponents for the real system will be difficult. Such problems pave the way for more operational definitions of dynamic complexity (cf. Yao & Tong, this volume) . Aside from its use in the characterization of chaos, nonlinear forecasting can be used more broadly in pragmatic classification problems. Here I review a recent example of nonlinear forecasting as it is applied to classify human heart rhythms. In particular, it is shown how forecast nonlinearity can be a good discriminator of the physiological effects of age, and how prediction-decay may discriminate heartdisease. In so doing, I introduce a method for characterizing nonlinearity using ‘S-maps’ and a method for analysing multiple short time series with composite attractors.

scholarly journals Detecting Predictable Segments of Chaotic Financial Time Series via Neural Network

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Tianle Zhou ◽  
Chaoyi Chu ◽  
Chaobin Xu ◽  
Weihao Liu ◽  
Hao Yu
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Phase Space ◽  
Financial Market ◽  
Financial Time Series ◽  
Influential Factors ◽  
Series Data ◽  
Phase Point ◽  
Price Fluctuations ◽  
Financial Time

In this study, a new idea is proposed to analyze the financial market and detect price fluctuations, by integrating the technology of PSR (phase space reconstruction) and SOM (self organizing maps) neural network algorithms. The prediction of price and index in the financial market has always been a challenging and significant subject in time-series studies, and the prediction accuracy or the sensitivity of timely warning price fluctuations plays an important role in improving returns and avoiding risks for investors. However, it is the high volatility and chaotic dynamics of financial time series that constitute the most significantly influential factors affecting the prediction effect. As a solution, the time series is first projected into a phase space by PSR, and the phase tracks are then sliced into several parts. SOM neural network is used to cluster the phase track parts and extract the linear components in each embedded dimension. After that, LSTM (long short-term memory) is used to test the results of clustering. When there are multiple linear components in the m-dimension phase point, the superposition of these linear components still remains the linear property, and they exhibit order and periodicity in phase space, thereby providing a possibility for time series prediction. In this study, the Dow Jones index, Nikkei index, China growth enterprise market index and Chinese gold price are tested to determine the validity of the model. To summarize, the model has proven itself able to mark the unpredictable time series area and evaluate the unpredictable risk by using 1-dimension time series data.

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