Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

Jacinta Muindi; George Muhua; Ronald Wanyonyi

doi:doi:10.11648/j.ajtas.20241306.13

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Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

Jacinta Muindi^*

, George Muhua

, Ronald Wanyonyi

Published in American Journal of Theoretical and Applied Statistics (Volume 13, Issue 6)

Received: 11 October 2024 Accepted: 4 November 2024 Published: 26 November 2024

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Abstract

The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.

Published in	American Journal of Theoretical and Applied Statistics (Volume 13, Issue 6)
DOI	10.11648/j.ajtas.20241306.13
Page(s)	203-212
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

Nonlinear Time Series, Threshold Autoregressive Models, SETAR, Bayesian Inference, Markov Chain Monte Carlo (MCMC), NSE20 Index

References

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[3]	Boero G., Lampis F. The Forecasting Performance of SETAR Models: An Empirical Application. Bulletin of Economic Research. 2017, 69(3), 216-228. https://doi.org/10.1111/boer.12068
[4]	Firat E. H. SETAR (Self-Exciting Threshold Autoregressive) Non-Linear Currency Modelling in EUR/USD, EUR/TRY and USD/TRY Parities. Mathematics and Statistics. 2017, 5(1), 33-55. https://doi.org/10.13189/ms.2017.050105
[5]	Gibson D., Nur D. Threshold Autoregressive Models in Finance: A Comparative Approach. In Proceedings of the Fourth Annual ASEARC Conference, University of Western Sydney, Paramatta, Australia, 2011; 18-23.
[6]	Oyewale A. M., Adelekan O. G., Innocient O. O. Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models. American Journal of Theoretical and Applied Statistics. 2017, 6(6), 278-283. https://doi.org/10.11648/j.ajtas.20170606.13
[7]	Tobechukwu N. M., Emmanuel B. O., Ibienebaka B. T. Self-Exciting Threshold Autoregressive Modelling of COVID-19 Confirmed Daily Cases in Nigeria. International Journal of Data Science and Analysis. 2022, 8(6), 182-186. https://doi.org/10.11648/j.ijdsa.20220806.12
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[12]	Andric V., Bodroza D., Djukic M. A Commentary on US Sovereign Debt Persistence and Nonlinear Fiscal Adjustment. Mathematics. 2024, 12(20), 3250. https://doi.org/10.3390/math12203250
[13]	Bolstad W. M., Curran J. M. Introduction to Bayesian statistics. John Wiley & Sons. 2016, 237-253. https://doi.org/10.1002/9781118593165
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APA Style

Muindi, J., Muhua, G., Wanyonyi, R. (2024). Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. American Journal of Theoretical and Applied Statistics, 13(6), 203-212. https://doi.org/10.11648/j.ajtas.20241306.13

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ACS Style

Muindi, J.; Muhua, G.; Wanyonyi, R. Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. Am. J. Theor. Appl. Stat. 2024, 13(6), 203-212. doi: 10.11648/j.ajtas.20241306.13

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AMA Style

Muindi J, Muhua G, Wanyonyi R. Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. Am J Theor Appl Stat. 2024;13(6):203-212. doi: 10.11648/j.ajtas.20241306.13

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@article{10.11648/j.ajtas.20241306.13,
  author = {Jacinta Muindi and George Muhua and Ronald Wanyonyi},
  title = {Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {6},
  pages = {203-212},
  doi = {10.11648/j.ajtas.20241306.13},
  url = {https://doi.org/10.11648/j.ajtas.20241306.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241306.13},
  abstract = {The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.
},
 year = {2024}
}

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TY  - JOUR
T1  - Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

AU  - Jacinta Muindi
AU  - George Muhua
AU  - Ronald Wanyonyi
Y1  - 2024/11/26
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241306.13
DO  - 10.11648/j.ajtas.20241306.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 203
EP  - 212
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241306.13
AB  - The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.

VL  - 13
IS  - 6
ER  -

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Author Information

Jacinta Muindi

Department of Mathematics, University of Nairobi, Nairobi, Kenya

Contact Email

http://orcid.org/0009-0002-2469-0141
George Muhua

Department of Mathematics, University of Nairobi, Nairobi, Kenya

Contact Email

http://orcid.org/0009-0002-7564-0363
Ronald Wanyonyi

Department of Mathematics, Egerton University, Nakuru, Kenya

Contact Email

http://orcid.org/0009-0000-3078-2144

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Plain Text BibTeX RIS

APA Style

Muindi, J., Muhua, G., Wanyonyi, R. (2024). Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. American Journal of Theoretical and Applied Statistics, 13(6), 203-212. https://doi.org/10.11648/j.ajtas.20241306.13

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ACS Style

Muindi, J.; Muhua, G.; Wanyonyi, R. Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. Am. J. Theor. Appl. Stat. 2024, 13(6), 203-212. doi: 10.11648/j.ajtas.20241306.13

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AMA Style

Muindi J, Muhua G, Wanyonyi R. Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach. Am J Theor Appl Stat. 2024;13(6):203-212. doi: 10.11648/j.ajtas.20241306.13

Copy | Download

@article{10.11648/j.ajtas.20241306.13,
  author = {Jacinta Muindi and George Muhua and Ronald Wanyonyi},
  title = {Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {6},
  pages = {203-212},
  doi = {10.11648/j.ajtas.20241306.13},
  url = {https://doi.org/10.11648/j.ajtas.20241306.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241306.13},
  abstract = {The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach

AU  - Jacinta Muindi
AU  - George Muhua
AU  - Ronald Wanyonyi
Y1  - 2024/11/26
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241306.13
DO  - 10.11648/j.ajtas.20241306.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 203
EP  - 212
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241306.13
AB  - The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.

VL  - 13
IS  - 6
ER  -

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