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Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

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  • Manimaran, P.
  • Panigrahi, Prasanta K.
  • Parikh, Jitendra C.

Abstract

We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multifractal detrended fluctuation analysis (MF-DFA) method and is quite accurate for small size data sets. As compared to polynomial fits in the MF-DFA, a single Daubechies wavelet is used here for detrending purposes. The natural, built-in variable window size in wavelet transforms makes this procedure well suited for non-stationary data. We illustrate the working of this method through the analysis of binomial multifractal model. For this model, our results compare well with those calculated analytically and obtained numerically through MF-DFA. To show the efficacy of this approach for finite data sets, we also do the above comparison for Gaussian white noise time series of different sizes. In addition, we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2D Ising model.

Suggested Citation

  • Manimaran, P. & Panigrahi, Prasanta K. & Parikh, Jitendra C., 2009. "Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2306-2314.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:12:p:2306-2314
    DOI: 10.1016/j.physa.2009.02.011
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    Cited by:

    1. Pal, Mayukha & Satish, B. & Srinivas, K. & Rao, P. Madhusudana & Manimaran, P., 2015. "Multifractal detrended cross-correlation analysis of coding and non-coding DNA sequences through chaos-game representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 596-603.
    2. Raza, Naveed & Jawad Hussain Shahzad, Syed & Tiwari, Aviral Kumar & Shahbaz, Muhammad, 2016. "Asymmetric impact of gold, oil prices and their volatilities on stock prices of emerging markets," Resources Policy, Elsevier, vol. 49(C), pages 290-301.
    3. Huang, Shupei & An, Haizhong & Gao, Xiangyun & Huang, Xuan, 2016. "Time–frequency featured co-movement between the stock and prices of crude oil and gold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 985-995.
    4. Ge, Xinlei & Lin, Aijing, 2021. "Multiscale multifractal detrended partial cross-correlation analysis of Chinese and American stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Das, Debojyoti & Bhowmik, Puja & Jana, R.K., 2018. "A multiscale analysis of stock return co-movements and spillovers: Evidence from Pacific developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 379-393.
    6. Pal, Mayukha & Madhusudana Rao, P. & Manimaran, P., 2014. "Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 452-460.
    7. Huang, Shupei & An, Haizhong & Gao, Xiangyun & Huang, Xuan, 2015. "Identifying the multiscale impacts of crude oil price shocks on the stock market in China at the sector level," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 13-24.
    8. Chowdhury, Mohammad Ashraful Ferdous & Meo, Muhammad Saeed & Uddin, Ajim & Haque, Md. Mahmudul, 2021. "Asymmetric effect of energy price on commodity price: New evidence from NARDL and time frequency wavelet approaches," Energy, Elsevier, vol. 231(C).
    9. Chen, Feier & Tian, Kang & Ding, Xiaoxu & Miao, Yuqi & Lu, Chunxia, 2016. "Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1058-1066.
    10. Vogl, Markus, 2023. "Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framewo," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    11. Manimaran, P. & Narayana, A.C., 2018. "Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 228-235.
    12. Pal, Debdatta & Mitra, Subrata K., 2017. "Time-frequency contained co-movement of crude oil and world food prices: A wavelet-based analysis," Energy Economics, Elsevier, vol. 62(C), pages 230-239.
    13. Ghosh, Sayantan & Manimaran, P. & Panigrahi, Prasanta K., 2011. "Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4304-4316.
    14. Pal, Mayukha & Kiran, V. Satya & Rao, P. Madhusudana & Manimaran, P., 2016. "Multifractal detrended cross-correlation analysis of genome sequences using chaos-game representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 288-293.
    15. Neeraj & Prasanta K. Panigrahi, 2016. "Causality and Correlations between BSE and NYSE indexes: A Janus Faced Relationship," Papers 1608.07796, arXiv.org.
    16. Vargas-Olmos, C. & Murguía, J.S. & Ramírez-Torres, M.T. & Mejía Carlos, M. & Rosu, H.C. & González-Aguilar, H., 2016. "Perceptual security of encrypted images based on wavelet scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 22-30.
    17. Kim, Hongseok & Oh, Gabjin & Kim, Seunghwan, 2011. "Multifractal analysis of the Korean agricultural market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4286-4292.
    18. Evrendilek, F. & Karakaya, N., 2014. "Regression model-based predictions of diel, diurnal and nocturnal dissolved oxygen dynamics after wavelet denoising of noisy time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 8-15.
    19. Neeraj, & Panigrahi, Prasanta K., 2017. "Causality and correlations between BSE and NYSE indexes: A Janus faced relationship," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 284-313.
    20. Sayantan Ghosh & P. Manimaran & Prasanta K. Panigrahi, 2010. "Characterizing Multi-Scale Self-Similar Behavior and Non-Statistical Properties of Financial Time Series," Papers 1003.2539, arXiv.org, revised Dec 2010.
    21. Chen, Feier & Miao, Yuqi & Tian, Kang & Ding, Xiaoxu & Li, Tingyi, 2017. "Multifractal cross-correlations between crude oil and tanker freight rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 344-354.

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