The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
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01 May 2016
TL;DR: A hybrid time-series ANFIS model based on EMD based on empirical mode decomposition (EMD) to forecast stock prices in the Taiwan Stock Exchange Capitalization Weighted Stock Index and Hang Seng Stock Index is proposed.
Abstract: This paper proposes a hybrid time-series ANFIS model based on EMD to forecast stock price.In order to evaluate the forecasting performances, the proposed model is compared with other models.The experimental results show that proposed model is superior to the listing models. Time series forecasting is an important and widely popular topic in the research of system modeling, and stock index forecasting is an important issue in time series forecasting. Accurate stock price forecasting is a challenging task in predicting financial time series. Time series methods have been applied successfully to forecasting models in many domains, including the stock market. Unfortunately, there are 3 major drawbacks of using time series methods for the stock market: (1) some models can not be applied to datasets that do not follow statistical assumptions; (2) most time series models that use stock data with a significant amount of noise involutedly (caused by changes in market conditions and environments) have worse forecasting performance; and (3) the rules that are mined from artificial neural networks (ANNs) are not easily understandable.To address these problems and improve the forecasting performance of time series models, this paper proposes a hybrid time series adaptive network-based fuzzy inference system (ANFIS) model that is centered around empirical mode decomposition (EMD) to forecast stock prices in the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Hang Seng Stock Index (HSI). To measure its forecasting performance, the proposed model is compared with Chen's model, Yu's model, the autoregressive (AR) model, the ANFIS model, and the support vector regression (SVR) model. The results show that our model is superior to the other models, based on root mean squared error (RMSE) values.
153 citations
TL;DR: A novel data-driven framework to estimate time-varying patterns of whole-brain functional network connectivity of resting state fMRI combined with the different frequencies and phase lags at which these patterns are observed is proposed.
153 citations
Cites background from "The empirical mode decomposition an..."
...Empirical mode decomposition (Huang et al., 1998), for example, estimates the instantaneous frequency of a given signal....
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TL;DR: A novel technique with morphological operators and fuzzy inference is proposed, which makes the algorithm to be able to detect early faults also and a new algorithm is proposed for this SE selection based on kurtosis, thereby making the analysis free of empirical methods.
Abstract: Bearing faults of rotating machinery are observed as impulses in the vibration signal, but it is mostly immersed in noise. In order to effectively remove this noise and detect the impulses, a novel technique with morphological operators and fuzzy inference is proposed in this paper. The effectiveness of the morphological operators lies with the correct selection of structuring elements (SEs). This paper also proposes a new algorithm for this SE selection based on kurtosis, thereby making the analysis free of empirical methods. When analyzed with three different sets of faults, the results show that this method is effective and robust in bringing out the impulses. With fuzzy inference being coupled to this new technique, it makes the algorithm to be able to detect early faults also.
153 citations
TL;DR: In this paper, a non-linear multivariate and multiscale statistical process monitoring and signal denoising method which combines the strengths of the Kernel Principal Component Analysis (KPCA) nonlinear multi-linear monitoring approach with the benefits of Ensemble Empirical Mode Decomposition (EEMD) is presented.
153 citations
TL;DR: In this article, Beijing PM2.5 and ISO-NE Dataset are analyzed by a novel Multivariate Temporal Convolution Network (M-TCN) model, which indicates significant improvement of prediction accuracy, robust and generalization of the model.
Abstract: Multivariable time series prediction has been widely studied in power energy, aerology, meteorology, finance, transportation, etc. Traditional modeling methods have complex patterns and are inefficient to capture long-term multivariate dependencies of data for desired forecasting accuracy. To address such concerns, various deep learning models based on Recurrent Neural Network (RNN) and Convolutional Neural Network (CNN) methods are proposed. To improve the prediction accuracy and minimize the multivariate time series data dependence for aperiodic data, in this article, Beijing PM2.5 and ISO-NE Dataset are analyzed by a novel Multivariate Temporal Convolution Network (M-TCN) model. In this model, multi-variable time series prediction is constructed as a sequence-to-sequence scenario for non-periodic datasets. The multichannel residual blocks in parallel with asymmetric structure based on deep convolution neural network is proposed. The results are compared with rich competitive algorithms of long short term memory (LSTM), convolutional LSTM (ConvLSTM), Temporal Convolution Network (TCN) and Multivariate Attention LSTM-FCN (MALSTM-FCN), which indicate significant improvement of prediction accuracy, robust and generalization of our model.
153 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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Book•
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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01 Jan 1946
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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