Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity

Josephine Njeri Ngure; Anthony Gichuhi Waititu; Simon Maina Mundia

doi:doi:10.11648/j.mcs.20251002.12

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Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity

Josephine Njeri Ngure^*, Anthony Gichuhi Waititu, Simon Maina Mundia

Published in Mathematics and Computer Science (Volume 10, Issue 2)

Received: 3 February 2025 Accepted: 19 March 2025 Published: 6 May 2025

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Abstract

This paper seeks to use the Moving Block Bootstrap method to determine the confidence intervals for a change point in conditional variance function of data exhibiting conditional heteroscedasticity and heterogeneity. Confidence intervals for a change point normally provide or give a range within which the true change point location is likely to lie. This is usually based on a specified confidence level. This helps to in turn determine whether the change point is statistically significant especially after determining the critical values for the distribution of the change point test statistic. Confidence intervals are also called interval estimates as opposed to point estimates which provide a single estimate for a parameter.

Published in	Mathematics and Computer Science (Volume 10, Issue 2)
DOI	10.11648/j.mcs.20251002.12
Page(s)	38-42
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), 2025. Published by Science Publishing Group

Keywords

Change Point, Bootstrap, Moving Block, Confidence Interval

References

[1]	Michael R Chernick. Bootstrap methods: A guide for practitioners and researchers, volume 619. John Wiley & Sons, 2011.
[2]	R Dennis Cook and Sanford Weisberg. Confidence curves in nonlinear regression. Journal of the American Statistical Association, 85(410): 544–551, 1990.
[3]	Alexandra Da Costa Dias and P Embrechts. Change- point analysis for dependence structures in finance and insurance. University of Leicester, 2004.
[4]	Bradley Efron and Robert J Tibshirani. An introduction to the bootstrap. Monographs on statistics and applied probability, 57: 1–436, 1993.
[5]	AW Gichuhi, J Franke, and JM Kihoro. Parametric change point estimation, testing and confidence interval applied in business. Journal of Agriculture, Science and Technology, 14(2): 136–148, 2012.
[6]	Hans R Künsch. The jackknife and the bootstrap for general stationary observations. Annals of Statiatics, 17 (3): 1217–1241, 1989.
[7]	Soumendra Nath Lahiri. Resampling methods for dependent data. Springer Science & Business Media, 2013.
[8]	Josephine Njeri Ngure, Anthony Gichuhi Waititu, and Simon Maina Mundia. Consistency of an estimator for change point in volatility of financial returns. Journal of Mathematics Research, 13 (1), 2021.
[9]	Josephine Njeri Ngure, Anthony Gichuhi Waititu, and Simon Maina Mundia. Detection and estimation of change point in volatility function of foreign exchange rate returns. International Journal of Data Science and Analysis, 9(1): 1–12, 2023. https://doi.org/10.11648/j.ijdsa.20230901.11

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APA Style

Ngure, J. N., Waititu, A. G., Mundia, S. M. (2025). Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Mathematics and Computer Science, 10(2), 38-42. https://doi.org/10.11648/j.mcs.20251002.12

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ACS Style

Ngure, J. N.; Waititu, A. G.; Mundia, S. M. Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Math. Comput. Sci. 2025, 10(2), 38-42. doi: 10.11648/j.mcs.20251002.12

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AMA Style

Ngure JN, Waititu AG, Mundia SM. Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Math Comput Sci. 2025;10(2):38-42. doi: 10.11648/j.mcs.20251002.12

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@article{10.11648/j.mcs.20251002.12,
  author = {Josephine Njeri Ngure and Anthony Gichuhi Waititu and Simon Maina Mundia},
  title = {Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity
},
  journal = {Mathematics and Computer Science},
  volume = {10},
  number = {2},
  pages = {38-42},
  doi = {10.11648/j.mcs.20251002.12},
  url = {https://doi.org/10.11648/j.mcs.20251002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20251002.12},
  abstract = {This paper seeks to use the Moving Block Bootstrap method to determine the confidence intervals for a change point in conditional variance function of data exhibiting conditional heteroscedasticity and heterogeneity. Confidence intervals for a change point normally provide or give a range within which the true change point location is likely to lie. This is usually based on a specified confidence level. This helps to in turn determine whether the change point is statistically significant especially after determining the critical values for the distribution of the change point test statistic. Confidence intervals are also called interval estimates as opposed to point estimates which provide a single estimate for a parameter.
},
 year = {2025}
}

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TY  - JOUR
T1  - Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity

AU  - Josephine Njeri Ngure
AU  - Anthony Gichuhi Waititu
AU  - Simon Maina Mundia
Y1  - 2025/05/06
PY  - 2025
N1  - https://doi.org/10.11648/j.mcs.20251002.12
DO  - 10.11648/j.mcs.20251002.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 38
EP  - 42
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20251002.12
AB  - This paper seeks to use the Moving Block Bootstrap method to determine the confidence intervals for a change point in conditional variance function of data exhibiting conditional heteroscedasticity and heterogeneity. Confidence intervals for a change point normally provide or give a range within which the true change point location is likely to lie. This is usually based on a specified confidence level. This helps to in turn determine whether the change point is statistically significant especially after determining the critical values for the distribution of the change point test statistic. Confidence intervals are also called interval estimates as opposed to point estimates which provide a single estimate for a parameter.

VL  - 10
IS  - 2
ER  -

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Author Information

Josephine Njeri Ngure

Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya

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Anthony Gichuhi Waititu

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya

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Simon Maina Mundia

Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya; Department of Statistics and Actuarial Sciences, Dedan Kimathi University of Technology (DEKUT), Nyeri, Kenya

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Plain Text BibTeX RIS

APA Style

Ngure, J. N., Waititu, A. G., Mundia, S. M. (2025). Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Mathematics and Computer Science, 10(2), 38-42. https://doi.org/10.11648/j.mcs.20251002.12

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ACS Style

Ngure, J. N.; Waititu, A. G.; Mundia, S. M. Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Math. Comput. Sci. 2025, 10(2), 38-42. doi: 10.11648/j.mcs.20251002.12

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AMA Style

Ngure JN, Waititu AG, Mundia SM. Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity. Math Comput Sci. 2025;10(2):38-42. doi: 10.11648/j.mcs.20251002.12

Copy | Download

@article{10.11648/j.mcs.20251002.12,
  author = {Josephine Njeri Ngure and Anthony Gichuhi Waititu and Simon Maina Mundia},
  title = {Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity
},
  journal = {Mathematics and Computer Science},
  volume = {10},
  number = {2},
  pages = {38-42},
  doi = {10.11648/j.mcs.20251002.12},
  url = {https://doi.org/10.11648/j.mcs.20251002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20251002.12},
  abstract = {This paper seeks to use the Moving Block Bootstrap method to determine the confidence intervals for a change point in conditional variance function of data exhibiting conditional heteroscedasticity and heterogeneity. Confidence intervals for a change point normally provide or give a range within which the true change point location is likely to lie. This is usually based on a specified confidence level. This helps to in turn determine whether the change point is statistically significant especially after determining the critical values for the distribution of the change point test statistic. Confidence intervals are also called interval estimates as opposed to point estimates which provide a single estimate for a parameter.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Moving Block Bootstrap Method for Determining Confidence Intervals for a Change Point in Time Series in the Presence of Conditional Heteroscedasticity

AU  - Josephine Njeri Ngure
AU  - Anthony Gichuhi Waititu
AU  - Simon Maina Mundia
Y1  - 2025/05/06
PY  - 2025
N1  - https://doi.org/10.11648/j.mcs.20251002.12
DO  - 10.11648/j.mcs.20251002.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 38
EP  - 42
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20251002.12
AB  - This paper seeks to use the Moving Block Bootstrap method to determine the confidence intervals for a change point in conditional variance function of data exhibiting conditional heteroscedasticity and heterogeneity. Confidence intervals for a change point normally provide or give a range within which the true change point location is likely to lie. This is usually based on a specified confidence level. This helps to in turn determine whether the change point is statistically significant especially after determining the critical values for the distribution of the change point test statistic. Confidence intervals are also called interval estimates as opposed to point estimates which provide a single estimate for a parameter.

VL  - 10
IS  - 2
ER  -

Copy | Download