scholarly journals SVD analysis of the magnetospheric AE index time series and comparison with low-dimensional chaotic dynamics

2001 ◽  
Vol 8 (1/2) ◽  
pp. 95-125 ◽  
Author(s):  
M. A. Athanasiu ◽  
G. P. Pavlos
Keyword(s):  
Time Series ◽  
Colored Noise ◽  
External Noise ◽  
Original Time Series ◽  
Svd Analysis ◽  
Ae Index ◽  
Low Dimensional ◽  
Original Time ◽  
Value Decomposition ◽  
Index Time Series

Abstract. The singular value decomposition (SVD) analysis is used at different stages in this paper in order to extract useful information concerning the underlying dynamics of the magnetospheric AE index. As a frame of reference we use the dynamics of the Lorenz system perturbed by external noise, white or colored. One of the critical results is that the colored noise can be differentiated from the white noise when we study their perturbation upon the eigenvalue spectrum of the trajectory matrix, the SVD reconstructed components of the original time series and other characteristics. This result is used in order to conclude the existence of strong component of colored noise included in the magnetospheric AE index time series. Moreover, the study of the SVD reconstructed components of the original time series can confirm the low-dimensionality of a dynamical system strongly perturbed by external colored noise. Finally, the results of this study strengthen the hypothesis of the magnetospheric chaos.

scholarly journals Chaos and magnetospheric dynamics

1994 ◽  
Vol 1 (2/3) ◽  
pp. 124-135 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Diamandidis ◽  
A. Adamopoulos ◽  
A. G. Rigas ◽  
I. A. Daglis ◽  
...  
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electric Circuit ◽  
Dynamical Chaos ◽  
Ae Index ◽  
Reconstructed Phase Space ◽  
Magnetospheric Dynamics ◽  
Low Dimensional ◽  
Value Decomposition ◽  
Index Time Series

Abstract. Our intention in this work is to show, by using two different methods, that magnetospheric dynamics reveal low dimensional chaos. In the first method we extend the chaotic analysis for the AE index time series by including singular value decomposition (SVD) analysis in combination with Theiler's test in order to discriminate dynamical chaos from self-affinity or "crinkliness". The estimated fractality of the AE index time series which is obtained belongs to a strange attractor structure with close returns in the reconstructed phase space. In the second method we extend the linear equivalent magnetospheric electric circuit to a nonlinear one, the arithmetic solution of which reveals low dimensional chaotic dynamics. Both methods strongly support the existence of low dimensional magnetospheric chaos.

INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

scholarly journals Nonlinear analysis of magnetospheric data Part II. Dynamical characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (2) ◽  
pp. 79-98 ◽  
Author(s):  
G. P. Pavlos ◽  
D. Kugiumtzis ◽  
M. A. Athanasiu ◽  
N. Hatzigeorgiu ◽  
D. Diamantidis ◽  
...  
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Dynamic Models ◽  
Surrogate Data ◽  
Dynamical Characteristics ◽  
Ae Index ◽  
The Family ◽  
Nonlinear Dynamic Models ◽  
Original Time ◽  
Index Time Series

Abstract. In this study we have used dynamical characteristies such as Lyapunov exponents, nonlinear dynamic models and mutual information for the nonlinear analysis of the magnetospheric AE index time series. Similarly with the geometrical characteristic studied in Pavlos et al. (1999b), we have found significant differences between the original time series and its surrogate data. These results also suggest the rejection of the null hypothesis that the AE index belongs to the family of stochastic linear signals undergoing a static nonlinear distortion. Finally, we believe that these results support the hypothesis of nonlinearity and chaos for the magnetospheric dynamics.

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

Precipitation Forecast Based on WA-SVM Theory

2012 ◽  
Vol 518-523 ◽  
pp. 4039-4042
Author(s):  
Zhen Min Zhou
Keyword(s):  
Time Series ◽  
Support Vector Machine ◽  
Wavelet Analysis ◽  
Precipitation Forecast ◽  
Support Vector ◽  
Estimation Model ◽  
Original Time Series ◽  
Set Up ◽  
Original Time

In order to improve the precision of medium-long term rainfall forecast, the rainfall estimation model was set up based on wavelet analysis and support vector machine (WA-SVM). It decomposed the original rainfall series to different layers through wavelet analysis, forecasted each layer by means of SVM, and finally obtained the forecast results of the original time series by composition. The model was used to estimate the monthly rainfall sequence in the watershed. Comparing with other method which only uses support vector machine(SVM), it indicates that the estimated accuracy was improved obviously.

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

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