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Applications of Hilbert–Huang transform to non‐stationary financial time series analysis

Author

Listed:
  • Norden E. Huang
  • Man‐Li Wu
  • Wendong Qu
  • Steven R. Long
  • Samuel S. P. Shen

Abstract

A new method, the Hilbert–Huang Transform (HHT), developed initially for natural and engineering sciences has now been applied to financial data. The HHT method is specially developed for analysing non‐linear and non‐stationary data. The method consists of two parts: (1) the empirical mode decomposition (EMD), and (2) the Hilbert spectral analysis. The key part of the method is the first step, the EMD, with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions (IMF). An IMF is defined here as any function having the same number of zero‐crossing and extrema, and also having symmetric envelopes defined by the local maxima, and minima respectively. The IMF also thus admits well‐behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non‐linear and non‐stationary processes. With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy–frequency–time distribution, which we designate as the Hilbert Spectrum. Comparisons with Wavelet and Fourier analyses show the new method offers much better temporal and frequency resolutions. The EMD is also useful as a filter to extract variability of different scales. In the present application, HHT has been used to examine the changeability of the market, as a measure of volatility of the market. Published in 2003 by John Wiley & Sons, Ltd.

Suggested Citation

  • Norden E. Huang & Man‐Li Wu & Wendong Qu & Steven R. Long & Samuel S. P. Shen, 2003. "Applications of Hilbert–Huang transform to non‐stationary financial time series analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(3), pages 245-268, July.
    • Handle: RePEc:wly:apsmbi:v:19:y:2003:i:3:p:245-268
    DOI: 10.1002/asmb.501
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    Cited by:

    1. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
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    3. Mahata, Ajit & Rai, Anish & Nurujjaman, Md. & Prakash, Om, 2021. "Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    4. Massouleh, S.H. Momeni & Kordkheili, S.A. Hosseini, 2019. "Experimental investigation of empirical mode decomposition by reduction of end effect error," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    5. Wang, Haoyu & Di, Junpeng & Yang, Zhaojun & Han, Qing, 2020. "Assessment of mutual fund performance based on Ensemble Empirical Mode Decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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    7. Xinchang Liu & Bolong Liu, 2023. "A Hybrid Time Series Model for Predicting the Displacement of High Slope in the Loess Plateau Region," Sustainability, MDPI, vol. 15(6), pages 1-26, March.
    8. Noemi Nava & T. Di Matteo & Tomaso Aste, 2015. "Anomalous volatility scaling in high frequency financial data," Papers 1503.08465, arXiv.org, revised Dec 2015.
    9. Ouyang, Fang-Yan & Zheng, Bo & Jiang, Xiong-Fei, 2019. "Dynamic fluctuations of cross-correlations in multi-time scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 515-521.
    10. Ftiti, Zied & Hadhri, Sinda, 2019. "Can economic policy uncertainty, oil prices, and investor sentiment predict Islamic stock returns? A multi-scale perspective," Pacific-Basin Finance Journal, Elsevier, vol. 53(C), pages 40-55.
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    12. Fang-Fang Li & Zhi-Yu Wang & Xiao Zhao & En Xie & Jun Qiu, 2019. "Decomposition-ANN Methods for Long-Term Discharge Prediction Based on Fisher’s Ordered Clustering with MESA," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(9), pages 3095-3110, July.
    13. Tim Leung & Theodore Zhao, 2021. "Multiscale Decomposition and Spectral Analysis of Sector ETF Price Dynamics," JRFM, MDPI, vol. 14(10), pages 1-22, October.
    14. Liu, Shuyu & Huang, Shupei & Chi, Yuxi & Feng, Sida & Li, Yang & Sun, Qingru, 2020. "Three-level network analysis of the North American natural gas price: A multiscale perspective," International Review of Financial Analysis, Elsevier, vol. 67(C).
    15. Zhongqi Shi & Rumian Zhong & Nan Jin, 2023. "Real-Time Tracking of Time-Varying Cable Frequency Based on a Time-Domain Signal Processing Method," Sustainability, MDPI, vol. 15(2), pages 1-12, January.
    16. Yuan-Chien Lin & En-Dian Kuo & Wan-Ju Chi, 2021. "Analysis of Meteorological Drought Resilience and Risk Assessment of Groundwater Using Signal Analysis Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 179-197, January.
    17. Cho, Jung-Hoon & Kim, Dong-Kyu & Kim, Eui-Jin, 2022. "Multi-scale causality analysis between COVID-19 cases and mobility level using ensemble empirical mode decomposition and causal decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    18. Jin, Xuejun & Zhu, Keer & Yang, Xiaolan & Wang, Shouyang, 2021. "Estimating the reaction of Bitcoin prices to the uncertainty of fiat currency," Research in International Business and Finance, Elsevier, vol. 58(C).
    19. Chen, Mu-Chen & Wei, Yu, 2011. "Exploring time variants for short-term passenger flow," Journal of Transport Geography, Elsevier, vol. 19(4), pages 488-498.
    20. Huang, Junwei & Xiao, Qingtai & Liu, Jingjing & Wang, Hua, 2019. "Modeling heat transfer properties in an ORC direct contact evaporator using RBF neural network combined with EMD," Energy, Elsevier, vol. 173(C), pages 306-316.
    21. Rai, Anish & Mahata, Ajit & Nurujjaman, Md & Majhi, Sushovan & Debnath, Kanish, 2022. "A sentiment-based modeling and analysis of stock price during the COVID-19: U- and Swoosh-shaped recovery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    22. Korotin, Vladimir & Dolgonosov, Maxim & Popov, Victor & Korotina, Olesya & Korolkova, Inna, 2019. "The Ukrainian crisis, economic sanctions, oil shock and commodity currency: Analysis based on EMD approach," Research in International Business and Finance, Elsevier, vol. 48(C), pages 156-168.
    23. Mahata, Ajit & Bal, Debi Prasad & Nurujjaman, Md, 2020. "Identification of short-term and long-term time scales in stock markets and effect of structural break," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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