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Wavelet methods in (financial) time-series processing

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  • Struzik, Zbigniew R.

Abstract

We briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the S&P index. In particular, we show how to uncover the local scaling (correlation) characteristics of the S&P index with the wavelet based effective Hölder exponent (Struzik, in: Fractals: Theory and Applications in Engineering, Dekking, Lévy Véhel, Lutton, Tricot, Springer, Berlin, 1999; Fractals 8 (2) (2000) 163). We use it to display the local spectral (multifractal) contents of the S&P index. In addition to this, we analyse the collective properties of the local correlation exponent as perceived by the trader, exercising various time horizon analyses of the index. We observe an intriguing interplay between such (different) time horizons. Heavy oscillations at shorter time horizons, which seem to be accompanied by a steady decrease of correlation level for longer time horizons, seem to be characteristic patterns before the biggest crashes of the index. We find that this way of local presentation of scaling properties may be of economic importance.

Suggested Citation

  • Struzik, Zbigniew R., 2001. "Wavelet methods in (financial) time-series processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 307-319.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:1:p:307-319
    DOI: 10.1016/S0378-4371(01)00101-7
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    4. Siab Mamipour & Sanaz Yazdani & Elmira Sepehri, 2022. "Examining the spillover effects of volatile oil prices on Iran’s stock market using wavelet-based multivariate GARCH model," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 46(4), pages 785-801, October.
    5. Li, Hui & Wu, Min & Wang, Xiao-Tian, 2009. "Fractional-moment Capital Asset Pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 412-421.
    6. Yiwen Cui & Lei Li & Zijie Tang, 2021. "Risk Analysis of China Stock Market During Economic Downturns–Based on GARCH-VaR and Wavelet Transformation Approaches," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 11(4), pages 322-336, April.
    7. He, Kaijian & Yu, Lean & Lai, Kin Keung, 2012. "Crude oil price analysis and forecasting using wavelet decomposed ensemble model," Energy, Elsevier, vol. 46(1), pages 564-574.
    8. Fernandez, Viviana & Lucey, Brian M., 2007. "Portfolio management under sudden changes in volatility and heterogeneous investment horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 612-624.
    9. 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).
    10. Avishek Bhandari, 2020. "A wavelet analysis of inter-dependence, contagion and long memory among global equity markets," Papers 2003.14110, arXiv.org.
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