scholarly journals MULTIFRACTAL CROSS WAVELET ANALYSIS

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750054 ◽  
Author(s):  
ZHI-QIANG JIANG ◽  
XING-LU GAO ◽  
WEI-XING ZHOU ◽  
H. EUGENE STANLEY
Keyword(s):  
Wavelet Analysis ◽  
Long Range ◽  
Cross Correlation ◽  
Multifractal Spectrum ◽  
Theoretical Formula ◽  
Cross Correlations ◽  
The Cross ◽  
Cross Wavelet Analysis ◽  
Multifractal Behavior ◽  
Cross Wavelet

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.

Analyzing the Impact of COVID-19 on the Cross-Correlations between Financial Search Engine Data and Movie Box Office

2020 ◽  
pp. 2150021
Author(s):  
Renyu Wang ◽  
Yujie Xie ◽  
Hong Chen ◽  
Guozhu Jia
Keyword(s):  
Financial Market ◽  
Cross Correlation ◽  
Multifractal Spectrum ◽  
Movie Industry ◽  
Box Office ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross ◽  
Google Search ◽  
The Impact

This paper explores the COVID-19 influences on the cross-correlation between the movie market and the financial market. The nonlinear cross-correlations between movie box office data and Google search volumes of financial terms such as Dow Jones Industrial Average (DJIA), NASDAQ and PMI are investigated based on multifractal detrended cross-correlation analysis (MF-DCCA). The empirical results show there are nonlinear cross-correlations between movie market and financial market. Metrics such as Hurst exponents, singular exponents and multifractal spectrum demonstrate that the cross-correlation between movie market and financial market is persistent, and the cross-correlation in long term is more stable than that in short term. In the COVID-19 period, the multifractal features of cross-correlation become stronger implying that COVID-19 enhanced the complexity between the movie industry and the financial market. Furthermore, through the rolling window analysis, the Hurst exponent dynamic trends indicate that COVID-19 has a clear influence on the cross-correlation between movie market and financial market.

scholarly journals Wavelet analysis of the magnetotail response to solar wind fluctuations during HILDCCA events

2019 ◽  
Author(s):  
Adriane Marques de Souza Franco ◽  
Ezequiel Echer ◽  
Mauricio José Alves Bolzan
Keyword(s):  
Solar Wind ◽  
Wavelet Transform ◽  
Wavelet Analysis ◽  
High Intensity ◽  
Geomagnetic Field ◽  
Long Duration ◽  
Analysis Technique ◽  
The Cross ◽  
Cross Wavelet Analysis ◽  
Cross Wavelet

Abstract. In this work a study of the effects of the High-Intensity Long-Duration Continuous AE activity events (HILDCAAs) in the magnetotail was conducted. The aim of this study was to search the main frequencies during HILDCAAs in the Bx component of the geomagnetic field, as well as at the main frequencies which the magnetotail responds to the solar wind during these events. In order to conduct this analysis the wavelet transform was employed in 9 HILDCAA events that occurred after the Cluster mission (2000) and coincided with the Cluster crossing through the tail of the magnetosphere from 2003 to 2007. Altogether, 25 most energetic periods was observed, which 76 % are ≤ 4 hours. The cross wavelet analysis technique was also used for the development of this study. It was applied to data of the Bz-IMF component and the Bx geomagnetic component, searching to obtain the periods in that had the highest correlation between these two series. To obtain these periods is important to identify frequencies on which the coupling of energy is stronger, as well the modulation of the magnetotail by the solar wind during HILDCAA events. The majority of correlation periods between the Bz (IMF) and Bx component of the geomagnetic field observed also were ≤ 4 hours, with 62.9 % of the periods. Thus the magnetotail responds stronger to IMF fluctuations during HILDCCAS at 2–4 hours scales, which are typical substorm periods.

ON THE CROSS WAVELET ANALYSIS OF DUFFING OSCILLATOR

1999 ◽  
Vol 228 (1) ◽  
pp. 199-210 ◽  
Author(s):  
A. KYPRIANOU ◽  
W.J. STASZEWSKI
Keyword(s):  
Wavelet Analysis ◽  
Duffing Oscillator ◽  
The Cross ◽  
Cross Wavelet Analysis ◽  
Cross Wavelet

scholarly journals Nitrous oxide fluxes over establishing biofuel crops: Characterization of temporal variability using the cross‐wavelet analysis

GCB Bioenergy ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 756-770
Author(s):  
Marcelo Zeri ◽  
Wendy H. Yang ◽  
Gisleine Cunha‐Zeri ◽  
Christy D. Gibson ◽  
Carl J. Bernacchi
Keyword(s):  
Nitrous Oxide ◽  
Wavelet Analysis ◽  
Temporal Variability ◽  
Biofuel Crops ◽  
The Cross ◽  
Cross Wavelet Analysis ◽  
Cross Wavelet

scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

scholarly journals Investigations of Broad Line Region Structure and Kinematics Using Variability

1989 ◽  
Vol 134 ◽  
pp. 93-95
Author(s):  
C. Martin Gaskell ◽  
Anuradha P. Koratkar ◽  
Linda S. Sparke
Keyword(s):  
Time Series ◽  
Cross Correlation ◽  
Sampling Interval ◽  
Broad Line ◽  
Line Flux ◽  
Line Region ◽  
Cross Correlations ◽  
The Mean ◽  
The Cross ◽  
The Continuum

Gaskell and Sparke (1986) showed that one can determine the sizes of BLRs more accurately that the mean sampling interval by cross-correlating the continuum flux time series with a line flux time series. The position of the peak in the cross-correlation function (CCF) and its shape give an indication of the BLR size. The technique is explained in detail in Gaskell and Peterson (1987). The widely propagated misunderstanding is that the method involves simply interpolating both time series and cross-correlating them (in which case the CCF is dominated by the cross-correlations of “made-up” data). Actually the method involves cross correlating the observed points in one time series (continuum, say) with the linear interpolations of the other series (line flux). The line flux time series must always be smoother than the continuum time series it is derived from. We have usually employed the method with the interpolation done both ways round and averaged them (to reduce errors due to the interpolation) and we can intercompare the two results (to investigate errors).

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