Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility

Rosemary Ukamaka Okafor; Josephine Nneamaka Onyeka-Ubaka

doi:doi:10.11648/j.ijsd.20230901.13

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Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility

Rosemary Ukamaka Okafor, Josephine Nneamaka Onyeka-Ubaka

Published in International Journal of Statistical Distributions and Applications (Volume 9, Issue 1)

Received: 20 January 2023 Accepted: 16 February 2023 Published: 27 February 2023

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Abstract

As a result of volatility dynamics, investors and other stakeholders in businesses and industries have difficulty making financial decisions. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are the most widely applied in the analysis of financial derivatives volatility. Volatility persistence is a common issue when analyzing stock prices, making it cumbersome for GARCH models. The GARCH model is transformed into the Makov switching GARCH model to check for dynamics in volatility persistence. Markov Regime-Switching GARCH (MSGARCH) models permit the conditional mean and variance to change across regimes over time. The Markov switching GARCH models incorporate the regime variables in the parameter space, making it viable for the parameters to be estimated by the maximum likelihood estimation method, unlike the classical GARCH models. Zenith Bank plc’s daily closing stock prices, a top-tier stock on the Nigerian Stock Exchange market, are fitted using the GARCH and MSGARCH models. The comparison between the MSGARCH model and the classical GARCH model was verified using the AIC and BIC metrics as well as the one with the maximum log likelihood estimates. The outcome suggests that MSGARCH model performs better than the single-regime GARCH model and that it yields significantly better out of-sample volatility forecasts. The results will aid the stakeholders to leverage and mitigate risks in their investment on the selected stocks.

Published in	International Journal of Statistical Distributions and Applications (Volume 9, Issue 1)
DOI	10.11648/j.ijsd.20230901.13
Page(s)	24-34
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

Volatility, GARCH Process, Regime-Switching, Markov Process, Maximum Likelihood Estimation

References

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[4]	Mikosch, T. and Starica, C. (2004). Non-stationarities in financial time series, the long-range dependence and the IGARCH Effects, Review of Economics and Statistics 86: 378-390.
[5]	Schwert, G. W. (1989). Why does stock market volatility change over time?, Journal of Finance 44: 1115-1153.
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[8]	Gray, S. F. (1996a). Modeling the conditional distribution of interest rates as a regime- switching process, Journal of Financial Economics 42: 27–62.
[9]	Chung-Ming Kuan. (2002). Lecture on the markov switching model, Institute of Economics Academia Sinica. Available at www.sinica.edu.tw/as/ssrc/ckuan.
[10]	Klaassen, F. J. G. M. (2002). Improving GARCH Volatility Forecasts with Regime-Switching GARCH. Advances in Markov-Switching Models 223-254.
[11]	Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31: 307-327.
[12]	Jason B. (2018). How to model volatility with ARCH and GARCH for time series forecasting in Python. Available at machinelearningmastery.com
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[17]	Mohd, Azizi Amin Nunian; Siti, Meriam Zahari and Sarifah, Radiah Shariff (2020). Modelling foreign exchange rates: a comparison between Markov-switching and Markov-switching GARCH, Journal of Electrical Engineering and Computer Science Vol. 20, No. 2: 917-923.
[18]	Onyeka-Ubaka, J. N., Ogundeji, R. K., Okafor, R. U. (2021). Time series filters applied to improve Box-Jenkins forecasting approach, Benin Journal of Statistics, ISSN 2682-5767. Vol.4: 31-52.
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Rosemary Ukamaka Okafor, Josephine Nneamaka Onyeka-Ubaka. (2023). Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. International Journal of Statistical Distributions and Applications, 9(1), 24-34. https://doi.org/10.11648/j.ijsd.20230901.13

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ACS Style

Rosemary Ukamaka Okafor; Josephine Nneamaka Onyeka-Ubaka. Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. Int. J. Stat. Distrib. Appl. 2023, 9(1), 24-34. doi: 10.11648/j.ijsd.20230901.13

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AMA Style

Rosemary Ukamaka Okafor, Josephine Nneamaka Onyeka-Ubaka. Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. Int J Stat Distrib Appl. 2023;9(1):24-34. doi: 10.11648/j.ijsd.20230901.13

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@article{10.11648/j.ijsd.20230901.13,
  author = {Rosemary Ukamaka Okafor and Josephine Nneamaka Onyeka-Ubaka},
  title = {Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {1},
  pages = {24-34},
  doi = {10.11648/j.ijsd.20230901.13},
  url = {https://doi.org/10.11648/j.ijsd.20230901.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230901.13},
  abstract = {As a result of volatility dynamics, investors and other stakeholders in businesses and industries have difficulty making financial decisions. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are the most widely applied in the analysis of financial derivatives volatility. Volatility persistence is a common issue when analyzing stock prices, making it cumbersome for GARCH models. The GARCH model is transformed into the Makov switching GARCH model to check for dynamics in volatility persistence. Markov Regime-Switching GARCH (MSGARCH) models permit the conditional mean and variance to change across regimes over time. The Markov switching GARCH models incorporate the regime variables in the parameter space, making it viable for the parameters to be estimated by the maximum likelihood estimation method, unlike the classical GARCH models. Zenith Bank plc’s daily closing stock prices, a top-tier stock on the Nigerian Stock Exchange market, are fitted using the GARCH and MSGARCH models. The comparison between the MSGARCH model and the classical GARCH model was verified using the AIC and BIC metrics as well as the one with the maximum log likelihood estimates. The outcome suggests that MSGARCH model performs better than the single-regime GARCH model and that it yields significantly better out of-sample volatility forecasts. The results will aid the stakeholders to leverage and mitigate risks in their investment on the selected stocks.},
 year = {2023}
}

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TY  - JOUR
T1  - Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility
AU  - Rosemary Ukamaka Okafor
AU  - Josephine Nneamaka Onyeka-Ubaka
Y1  - 2023/02/27
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230901.13
DO  - 10.11648/j.ijsd.20230901.13
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 24
EP  - 34
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230901.13
AB  - As a result of volatility dynamics, investors and other stakeholders in businesses and industries have difficulty making financial decisions. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are the most widely applied in the analysis of financial derivatives volatility. Volatility persistence is a common issue when analyzing stock prices, making it cumbersome for GARCH models. The GARCH model is transformed into the Makov switching GARCH model to check for dynamics in volatility persistence. Markov Regime-Switching GARCH (MSGARCH) models permit the conditional mean and variance to change across regimes over time. The Markov switching GARCH models incorporate the regime variables in the parameter space, making it viable for the parameters to be estimated by the maximum likelihood estimation method, unlike the classical GARCH models. Zenith Bank plc’s daily closing stock prices, a top-tier stock on the Nigerian Stock Exchange market, are fitted using the GARCH and MSGARCH models. The comparison between the MSGARCH model and the classical GARCH model was verified using the AIC and BIC metrics as well as the one with the maximum log likelihood estimates. The outcome suggests that MSGARCH model performs better than the single-regime GARCH model and that it yields significantly better out of-sample volatility forecasts. The results will aid the stakeholders to leverage and mitigate risks in their investment on the selected stocks.
VL  - 9
IS  - 1
ER  -

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Author Information

Rosemary Ukamaka Okafor

Department of Statistics, Faculty of Science, University of Lagos, Akoka, Nigeria
Josephine Nneamaka Onyeka-Ubaka

Department of Statistics, Faculty of Science, University of Lagos, Akoka, Nigeria

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Plain Text BibTeX RIS

APA Style

Rosemary Ukamaka Okafor, Josephine Nneamaka Onyeka-Ubaka. (2023). Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. International Journal of Statistical Distributions and Applications, 9(1), 24-34. https://doi.org/10.11648/j.ijsd.20230901.13

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ACS Style

Rosemary Ukamaka Okafor; Josephine Nneamaka Onyeka-Ubaka. Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. Int. J. Stat. Distrib. Appl. 2023, 9(1), 24-34. doi: 10.11648/j.ijsd.20230901.13

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AMA Style

Rosemary Ukamaka Okafor, Josephine Nneamaka Onyeka-Ubaka. Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility. Int J Stat Distrib Appl. 2023;9(1):24-34. doi: 10.11648/j.ijsd.20230901.13

Copy | Download

@article{10.11648/j.ijsd.20230901.13,
  author = {Rosemary Ukamaka Okafor and Josephine Nneamaka Onyeka-Ubaka},
  title = {Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {1},
  pages = {24-34},
  doi = {10.11648/j.ijsd.20230901.13},
  url = {https://doi.org/10.11648/j.ijsd.20230901.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230901.13},
  abstract = {As a result of volatility dynamics, investors and other stakeholders in businesses and industries have difficulty making financial decisions. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are the most widely applied in the analysis of financial derivatives volatility. Volatility persistence is a common issue when analyzing stock prices, making it cumbersome for GARCH models. The GARCH model is transformed into the Makov switching GARCH model to check for dynamics in volatility persistence. Markov Regime-Switching GARCH (MSGARCH) models permit the conditional mean and variance to change across regimes over time. The Markov switching GARCH models incorporate the regime variables in the parameter space, making it viable for the parameters to be estimated by the maximum likelihood estimation method, unlike the classical GARCH models. Zenith Bank plc’s daily closing stock prices, a top-tier stock on the Nigerian Stock Exchange market, are fitted using the GARCH and MSGARCH models. The comparison between the MSGARCH model and the classical GARCH model was verified using the AIC and BIC metrics as well as the one with the maximum log likelihood estimates. The outcome suggests that MSGARCH model performs better than the single-regime GARCH model and that it yields significantly better out of-sample volatility forecasts. The results will aid the stakeholders to leverage and mitigate risks in their investment on the selected stocks.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Analyzing Dynamic Regimes of GARCH Model on Stock Price Volatility
AU  - Rosemary Ukamaka Okafor
AU  - Josephine Nneamaka Onyeka-Ubaka
Y1  - 2023/02/27
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230901.13
DO  - 10.11648/j.ijsd.20230901.13
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 24
EP  - 34
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230901.13
AB  - As a result of volatility dynamics, investors and other stakeholders in businesses and industries have difficulty making financial decisions. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are the most widely applied in the analysis of financial derivatives volatility. Volatility persistence is a common issue when analyzing stock prices, making it cumbersome for GARCH models. The GARCH model is transformed into the Makov switching GARCH model to check for dynamics in volatility persistence. Markov Regime-Switching GARCH (MSGARCH) models permit the conditional mean and variance to change across regimes over time. The Markov switching GARCH models incorporate the regime variables in the parameter space, making it viable for the parameters to be estimated by the maximum likelihood estimation method, unlike the classical GARCH models. Zenith Bank plc’s daily closing stock prices, a top-tier stock on the Nigerian Stock Exchange market, are fitted using the GARCH and MSGARCH models. The comparison between the MSGARCH model and the classical GARCH model was verified using the AIC and BIC metrics as well as the one with the maximum log likelihood estimates. The outcome suggests that MSGARCH model performs better than the single-regime GARCH model and that it yields significantly better out of-sample volatility forecasts. The results will aid the stakeholders to leverage and mitigate risks in their investment on the selected stocks.
VL  - 9
IS  - 1
ER  -

Copy | Download