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Long Memory and Fractality Among Global Equity Markets: a Multivariate Wavelet Approach

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Abstract

This paper seeks to understand the long memory behaviour of global equity returns using novel methods from wavelet analysis. We implement the wavelet based multivariate long memory approach, which possibly is the first application of wavelet based multivariate long memory technique in finance and economics. In doing so, long-run correlation structures among global equity returns are captured within the framework of wavelet-multivariate long memory methods, enabling one to analyze the long-run correlation among several markets exhibiting both similar and dissimilar fractal structures.

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Notes

  1. This is not to be confused with the regular wavelet correlation where correlations tend to be strong in the long-run. Correlations based on fractal connectivity are used to determine the similarity in mechanisms that generate the underlying long memory behaviour among markets.

  2. Wavelet correlation and cross-correlations are like the usual cross-spectral meaures from spectral analysis. However, cross-spectral methods cannot capture the time component as it relies on Fourier decomposition of time signal wherein time information is completely lost, which is not the case with wavelet based decompositions where information from both time and frequencies are captured or localized simultaneously.

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Acknowledgement

Computations are done in both MATLAB and R Programming language. The authors would like to thank Prof. Darryl Veitch for providing the MATLAB program which can be accessed from https://crin.eng.uts.edu.au/~darryl/secondorder_code.html. The R codes written by the authors are based on multiwave and fArma packages in R. The dataset used along with the codes, which can replicate results of this paper, shall be provided by the corresponding author on request.

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Authors and Affiliations

  1. Department of General Management, Institute of Management Technology, No. 38, Cherlaguda Village, Shamshabad Mandal, RR District, Hyderabad, 501218, India

    Avishek Bhandari

  2. School of Management Studies, University of Hyderabad, Hyderabad, 500046, India

    Bandi Kamaiah

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  1. Avishek Bhandari
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  2. Bandi Kamaiah
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Correspondence to Avishek Bhandari.

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Bhandari, A., Kamaiah, B. Long Memory and Fractality Among Global Equity Markets: a Multivariate Wavelet Approach. J. Quant. Econ. 19, 23–37 (2021). https://doi.org/10.1007/s40953-020-00220-0

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