Wavelet Transform Modulus Maxima Approach for World Stock Index Multifractal Analysis

Pučkovs, Andrejs; Matvejevs, Andrejs

doi:10.2478/v10313-012-0016-5

Cited by 9 publications

(13 citation statements)

References 3 publications

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“…Because of its capability of decomposing a signal into small fractions that are well localized in time and frequency and detecting local irregularities of a signal (areas of the signal where a particular derivative is not continuous) such as nonstationarity, oscillatory behaviour, breakdown, discontinuity in higher derivatives, the presence of long-range dependence, and other trends (Maruyama 2016b;Puckovs & Matvejevs 2012), wavelet analysis remains one of the most preferred signal analysis techniques to date. Additionally, there is a claim that wavelet transforms are suitable for multifractal analysis and allow reliable multifractal analysis to be performed (Muzy et al 1991).…”

Section: Methods and Proceduresmentioning

confidence: 99%

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Revealing the non-linear behaviour of the lensed quasar Q0957+561

Belete

Martins

Leão

et al. 2019

Monthly Notices of the Royal Astronomical Society

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Knowledge about how the nonlinear behaviour of the intrinsic signal from lensed background sources changes on its path to the observer provides much information, particularly about the matter distribution in lensing galaxies and the physical properties of the current universe, in general. Here, we analyse the multifractal (nonlinear) behaviour of the optical observations of A and B images of Q0957+561 in the r and g bands. AIMS: To verify the presence, or absence, of extrinsic variations in the observed signals of the quasar images and investigate whether extrinsic variations affect the multifractal behaviour of their intrinsic signals. METHOD: We apply a wavelet transform modulus maxima-based multifractality analysis approach. RESULTS: We detect strong multifractal (nonlinear) signatures in the light curves of the quasar images. The degree of multifractality for both images in the r band changes over time in a non-monotonic way, possibly indicating the presence of extrinsic variabilities in the light curves of the images, i.e., the signals of the quasar images are a combination of both intrinsic and extrinsic signals. Additionally, in the r band, in periods of quiescent microlensing activity, we find that the degree of multifractality (nonlinearity) of image A is stronger than that of B, while B has a larger multifractal strength in recent epochs (from day 5564 to day 7527) when it appears to be affected by microlensing. Finally, comparing the optical bands in a period of quiescent microlensing activity, we find that the degree of multifractality is stronger in the r band for both quasar images. In the absence of microlensing, the observed excesses of nonlinearity are most likely generated when the broad-line region (BLR) reprocesses the radiation from the compact sources.

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Section: Methods and Proceduresmentioning

confidence: 99%

“…Here, we apply WTMM-based multifractality analysis, which was originally introduced by Muzy et al (1991). We follow the procedures discussed by Puckovs & Matvejevs (2012): 1. We calculate wavelet coefficients of the signal X(t) using the following mathematical relation:…”

Section: Methods and Proceduresmentioning

confidence: 99%

Revealing the non-linear behaviour of the lensed quasar Q0957+561

Belete

Martins

Leão

et al. 2019

Monthly Notices of the Royal Astronomical Society

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“…It can partition the time and scale domain of a signal into fractal dimension regions. This method is also referred to as a "mathematical microscope" due to its ability to inspect the multi-scale dimensional characteristics of a signal and possibly inform about the sources of these characteristics [6]. At local time 11:56:25 am NST of 25 April 2015, an earthquake of MW 7.8 struck at Nepal (www.usgs.gov/news/magnitude-78-earthquake-nepal -aftershocks).…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis for seismic wave in Kathmandu valley after Gorkha Earthquake-2015, Nepal

Tiwari

Adhikari

et al. 2020

J. Nep. Phys. Soc.

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We applied the multiscale signal processing technique, the Wavelet Transform Modulus Maxima (WTMM) to characterize high frequency properties of strong motion waveforms, in particular the temporal distribution and strength of singularities in Gorkha earthquake, 25th April 2015. We first explored their relation to earthquake data source. Then we applied the WTMM analysis to strong motion recordings. These showed that the timing and exponent of singularities measured by the WTMM method on the ground motion wave field are directly related to the position and exponent of assumed initial stress singularities on the fault plane. We found strong motion recordings at near the epicenter site have very high multifractality than far sites. Some differences and similarities among sites were successfully detected.

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“…This method is based on wavelet analysis that is called -mathematical microscope‖ due to its ability to maintain good resolution at different scales [18]. The WTMM method is a powerful tool for statistical description of non-stationary signals, because the wavelet functions are localized in time and frequency.…”

Section: Wavelet Transform Modulus Maximamentioning

confidence: 99%

Analysis of Heart Rate Variability by Applying Nonlinear Methods with Different Approaches for Graphical Representation of Results

Gospodinova¹,

Gospodinov²,

Domuschiev³

et al. 2015

ijacsa

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Abstract-There is an open discussion over nonlinear properties of the Heart Rate Variability (HRV) which takes place in most scientific studies nowadays. The HRV analysis is a noninvasive and effective tool that manages to reflect the autonomic nervous system regulation of the heart. The current study presents the results of HRV analysis based on 24-hour Holter ECG signals of healthy and unhealthy subjects. Analysis of heart intervals is performed with the use of original algorithms and software, developed by the authors, to quantify the irregularity of the heart rate. The main aim is the formation of the parametric estimate of patients' health status, based on mathematical methods that are applied on cardiac physiology. The obtained results show that the analysis of Holter recordings by nonlinear methods may be appropriate for diagnostic, forecast and prevention of the pathological cardiac statuses. Different approaches of graphical representation and visualization of these results are used in order to verify this.

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Wavelet Transform Modulus Maxima Approach for World Stock Index Multifractal Analysis

Cited by 9 publications

References 3 publications

Revealing the non-linear behaviour of the lensed quasar Q0957+561

Revealing the non-linear behaviour of the lensed quasar Q0957+561

Multifractal analysis for seismic wave in Kathmandu valley after Gorkha Earthquake-2015, Nepal

Analysis of Heart Rate Variability by Applying Nonlinear Methods with Different Approaches for Graphical Representation of Results

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