Hurst Exponent Analysis on the Ghana Stock Exchange

Isaac Ampofi; Akyene Tetteh; Eric Neebo Wiah; Sampson Takyi Appiah

doi:doi:10.11648/j.ajmcm.20200503.13

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Hurst Exponent Analysis on the Ghana Stock Exchange

Isaac Ampofi, Akyene Tetteh, Eric Neebo Wiah, Sampson Takyi Appiah

Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)

Received: 29 May 2020 Accepted: 11 June 2020 Published: 25 August 2020

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Abstract

This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.

Published in	American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)
DOI	10.11648/j.ajmcm.20200503.13
Page(s)	77-82
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Stock Price, Hurst Exponent, Geometric Brownian Motion, Geometric Fractional Brownian Motion, Ghana Stock Exchange, Drift, Volatility, Ghana Commercial Bank

References

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[2]	Damptey, K. N. O. (2017), Rethinking the role of indigenous governance practices in contemporary governance in Africa, the case of Ghana.
[3]	Quayesam, D. L. (2016), Stochastic Modelling of Stock Prices on The Ghana Stock Exchange (Doctoral dissertation, University of Ghana).
[4]	Zili, M. (2006), on the mixed fractional Brownian motion. International Journal of Stochastic Analysis.
[5]	Bekaert, G., Harvey, C. R. and Lundblad, C. T. (2003), Equity market liberalization in emerging markets. Journal of Financial Research, 26, (3), pp. 275-299.
[6]	Jamdee, S. and Los, C. A. (2005) Long memory options: Valuation. Available at SSRN 588862.
[7]	Jamdee, S. and Los, C. A., (2007), Long memory options: LM evidence and simulations, Research in International Business and Finance, 21, (2), pp. 260-280.
[8]	Fortune, P., (1991), Stock market efficiency: an autopsy. New England Economic Review, pp. 17-40.
[9]	Gupta, K. and Singh, B., (2006), Random walk and indian equity futures market. In Indian Institute of Capital Markets 9th Capital Markets Conference Paper.
[10]	Afego, P. N. (2015), Market efficiency in developing African stock markets: what do we know? The Journal of Developing Areas, pp. 243-266.
[11]	Osei, K. A., (2006), Macroeconomic factors and the Ghana stock market, African finance journal, 8, (1), pp. 26-38.
[12]	Ntim, C. G., Opong, K. K. and Danbolt, J., (2007), An emperical re-examination of the weak form efficient markets hypothesis of the Ghana Stock Market using variance-ratios tests, African Finance Journal, 9, (2), pp. 1-25.
[13]	Adobaw, I., (2014), TESTING THE WEAK FORM MARKET EFFICIENCY OF SELECTED AFRICAN STOCK MARKETS (Doctoral dissertation, Department of Economics of the Faculty of Social Sciences, University of Cape Coast).
[14]	Boes, D. C. and Salas, J. D., (1978), Nonstationarity of the mean and the Hurst phenomenon, Water Resources Research, 14, (1), pp. 135-143.
[15]	Gursakal, N., Aydin, Z. B., Gursakal, S. and Tuzunturk, S., (2009), Hurst exponent analysis in Turkish stock market. International Journal of Sustainable Economy, 1, (3), pp. 255-269.
[16]	Mishura, I. S., Mishura, I. S., Misura, J. S., Mishura, Y. and Misura, U. S., (2008), Stochastic calculus for fractional Brownian motion and related processes, Springer Science and Business Media.
[17]	Biagini, F., Hu, Y., Oksendal, B. and Zhang T., (2008), Stochastic calculus for fractional Brownian motion and applications, Springer Science and Business Media.

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APA Style

Isaac Ampofi, Akyene Tetteh, Eric Neebo Wiah, Sampson Takyi Appiah. (2020). Hurst Exponent Analysis on the Ghana Stock Exchange. American Journal of Mathematical and Computer Modelling, 5(3), 77-82. https://doi.org/10.11648/j.ajmcm.20200503.13

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ACS Style

Isaac Ampofi; Akyene Tetteh; Eric Neebo Wiah; Sampson Takyi Appiah. Hurst Exponent Analysis on the Ghana Stock Exchange. Am. J. Math. Comput. Model. 2020, 5(3), 77-82. doi: 10.11648/j.ajmcm.20200503.13

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AMA Style

Isaac Ampofi, Akyene Tetteh, Eric Neebo Wiah, Sampson Takyi Appiah. Hurst Exponent Analysis on the Ghana Stock Exchange. Am J Math Comput Model. 2020;5(3):77-82. doi: 10.11648/j.ajmcm.20200503.13

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@article{10.11648/j.ajmcm.20200503.13,
  author = {Isaac Ampofi and Akyene Tetteh and Eric Neebo Wiah and Sampson Takyi Appiah},
  title = {Hurst Exponent Analysis on the Ghana Stock Exchange},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {3},
  pages = {77-82},
  doi = {10.11648/j.ajmcm.20200503.13},
  url = {https://doi.org/10.11648/j.ajmcm.20200503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200503.13},
  abstract = {This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.},
 year = {2020}
}

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TY  - JOUR
T1  - Hurst Exponent Analysis on the Ghana Stock Exchange
AU  - Isaac Ampofi
AU  - Akyene Tetteh
AU  - Eric Neebo Wiah
AU  - Sampson Takyi Appiah
Y1  - 2020/08/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200503.13
DO  - 10.11648/j.ajmcm.20200503.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 77
EP  - 82
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200503.13
AB  - This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.
VL  - 5
IS  - 3
ER  -

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Author Information

Isaac Ampofi

Mathematical Sciences Department, University of Mines and Technology, Tarkwa, Ghana
Akyene Tetteh

Management Studies Department, University of Mines and Technology, Tarkwa, Ghana
Eric Neebo Wiah

Mathematical Sciences Department, University of Mines and Technology, Tarkwa, Ghana
Sampson Takyi Appiah

Mathematics and Statistics Department, University of Energy and Natural Resources, Sunyani, Ghana

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Plain Text BibTeX RIS

APA Style

Isaac Ampofi, Akyene Tetteh, Eric Neebo Wiah, Sampson Takyi Appiah. (2020). Hurst Exponent Analysis on the Ghana Stock Exchange. American Journal of Mathematical and Computer Modelling, 5(3), 77-82. https://doi.org/10.11648/j.ajmcm.20200503.13

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ACS Style

Isaac Ampofi; Akyene Tetteh; Eric Neebo Wiah; Sampson Takyi Appiah. Hurst Exponent Analysis on the Ghana Stock Exchange. Am. J. Math. Comput. Model. 2020, 5(3), 77-82. doi: 10.11648/j.ajmcm.20200503.13

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AMA Style

Isaac Ampofi, Akyene Tetteh, Eric Neebo Wiah, Sampson Takyi Appiah. Hurst Exponent Analysis on the Ghana Stock Exchange. Am J Math Comput Model. 2020;5(3):77-82. doi: 10.11648/j.ajmcm.20200503.13

Copy | Download

@article{10.11648/j.ajmcm.20200503.13,
  author = {Isaac Ampofi and Akyene Tetteh and Eric Neebo Wiah and Sampson Takyi Appiah},
  title = {Hurst Exponent Analysis on the Ghana Stock Exchange},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {3},
  pages = {77-82},
  doi = {10.11648/j.ajmcm.20200503.13},
  url = {https://doi.org/10.11648/j.ajmcm.20200503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200503.13},
  abstract = {This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Hurst Exponent Analysis on the Ghana Stock Exchange
AU  - Isaac Ampofi
AU  - Akyene Tetteh
AU  - Eric Neebo Wiah
AU  - Sampson Takyi Appiah
Y1  - 2020/08/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200503.13
DO  - 10.11648/j.ajmcm.20200503.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 77
EP  - 82
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200503.13
AB  - This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.
VL  - 5
IS  - 3
ER  -

Copy | Download