THE TIME-DEPENDENT INTRINSIC CORRELATION BASED ON THE EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 02 (02) ◽  
pp. 233-265 ◽  
Author(s):  
XIANYAO CHEN ◽  
ZHAOHUA WU ◽  
NORDEN E. HUANG
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Empirical Mode Decomposition ◽  
Sliding Window ◽  
Time Dependent ◽  
New Approach ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Time Dependent Intrinsic Correlation ◽  
Intrinsic Correlation

A Time-Dependent Intrinsic Correlation (TDIC) method is introduced. This new approach includes both auto- and cross-correlation analysis designed especially to analyze, capture and track the local correlations between nonlinear and nonstationary time series pairs. The approach is based on Empirical Mode Decomposition (EMD) to decompose the nonlinear and nonstationary data into their intrinsic mode functions (IMFs) and uses the instantaneous periods of the IMFs to determine a set of the sliding window sizes for the computation of the running correlation coefficients for multi-scale data. This new method treats the selection of the sliding window sizes as an adaptive process determined by the data itself, not a "tuning" process. Therefore, it gives an intrinsic correlation analysis of the data. Furthermore, the multi-window approach makes the new method applicable to complicated data from multi-scale phenomena. The synthetic and time series from real world are used to demonstrate conclusively that the new approach is far more superior over the traditional method in its ability to reveal detailed and subtle correlations unavailable through any other methods in existence. Thus, the TDIC represents a major advance in statistical analysis of data from nonlinear and nonstationary processes.

scholarly journals A New Approach to Stochastically Generating Six-Monthly Rainfall Sequences Based on Empirical Mode Decomposition

2008 ◽  
Vol 9 (6) ◽  
pp. 1377-1389 ◽  
Author(s):  
Thomas A. McMahon ◽  
Anthony S. Kiem ◽  
Murray C. Peel ◽  
Phillip W. Jordan ◽  
Geoffrey G. S. Pegram
Keyword(s):  
Climate Change ◽  
Time Series ◽  
Empirical Mode Decomposition ◽  
Southern Oscillation ◽  
Monthly Rainfall ◽  
Anthropogenic Climate Change ◽  
New Approach ◽  
Mode Decomposition ◽  
Natural Climate ◽  
The Impact

Abstract This paper introduces a new approach to stochastically generating rainfall sequences that can take into account natural climate phenomena, such as the El Niño–Southern Oscillation and the interdecadal Pacific oscillation. The approach is also amenable to modeling projected affects of anthropogenic climate change. The method uses a relatively new technique, empirical mode decomposition (EMD), to decompose a historical rainfall series into several independent time series that have different average periods and amplitudes. These time series are then recombined to form an intradecadal time series and an interdecadal time series. After separate stochastic generation of these two series, because they are independent, they can be recombined by summation to form a replicate equivalent to the historical data. The approach was applied to generate 6-monthly rainfall totals for six rainfall stations located near Canberra, Australia. The cross correlations were preserved by carrying out the stochastic analysis using the Matalas multisite model. The results were compared with those obtained using a traditional autoregressive lag-one [AR(1)], and it was found that the new EMD stochastic model performed satisfactorily. The new approach is able to realistically reproduce multiyear–multidecadal dry and wet epochs that are characteristic of Australia’s climate and are not satisfactorily modeled using traditional stochastic rainfall generation methods. The method has two advantages over the traditional AR(1) approach, namely, that it can simulate nonstationarity characteristics in the historical time series, and it is easy to alter the decomposed time series components to examine the impact of anthropogenic climate change.

scholarly journals On the multi-scale nature of large geomagnetic storms: an empirical mode decomposition analysis

2012 ◽  
Vol 19 (6) ◽  
pp. 667-673 ◽  
Author(s):  
P. De Michelis ◽  
G. Consolini ◽  
R. Tozzi
Keyword(s):  
Time Series ◽  
Empirical Mode Decomposition ◽  
Geomagnetic Activity ◽  
Geomagnetic Storms ◽  
Decomposition Analysis ◽  
Activity Level ◽  
Activity Levels ◽  
Geomagnetic Disturbances ◽  
Multi Scale ◽  
Mode Decomposition

Abstract. Complexity and multi-scale are very common properties of several geomagnetic time series. On the other hand, it is amply demonstrated that scaling properties of geomagnetic time series show significant changes depending on the geomagnetic activity level. Here, we study the multi-scale features of some large geomagnetic storms by applying the empirical mode decomposition technique. This method, which is alternative to traditional data analysis and is designed specifically for analyzing nonlinear and nonstationary data, is applied to long time series of Sym-H index relative to periods including large geomagnetic disturbances. The spectral and scaling features of the intrinsic mode functions (IMFs) into which Sym-H time series can be decomposed, as well as those of the Sym-H time series itself, are studied considering different geomagnetic activity levels. The results suggest an increase of dynamical complexity and multi-scale properties for intermediate geomagnetic activity levels.

scholarly journals Intrinsic multi-scale analysis: a multi-variate empirical mode decomposition framework

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140709 ◽  
Author(s):  
David Looney ◽  
Apit Hemakom ◽  
Danilo P. Mandic
Keyword(s):  
Empirical Mode Decomposition ◽  
Data Driven ◽  
Estimation Methods ◽  
Scale Level ◽  
Standard Data ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Intrinsic Correlation ◽  
Feature Relevance ◽  
Intrinsic Scale

A novel multi-scale approach for quantifying both inter- and intra-component dependence of a complex system is introduced. This is achieved using empirical mode decomposition (EMD), which, unlike conventional scale-estimation methods, obtains a set of scales reflecting the underlying oscillations at the intrinsic scale level. This enables the data-driven operation of several standard data-association measures (intrinsic correlation, intrinsic sample entropy (SE), intrinsic phase synchrony) and, at the same time, preserves the physical meaning of the analysis. The utility of multi-variate extensions of EMD is highlighted, both in terms of robust scale alignment between system components, a pre-requisite for inter-component measures, and in the estimation of feature relevance. We also illuminate that the properties of EMD scales can be used to decouple amplitude and phase information, a necessary step in order to accurately quantify signal dynamics through correlation and SE analysis which are otherwise not possible. Finally, the proposed multi-scale framework is applied to detect directionality, and higher order features such as coupling and regularity, in both synthetic and biological systems.

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