Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics

Latifat Adebisi Abimbola; Taiwo Mobolaji Adegoke; Oladapo Muyiwa Oladoja

doi:doi:10.11648/j.ajtas.20241305.16

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Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics

Latifat Adebisi Abimbola^*

, Taiwo Mobolaji Adegoke

, Oladapo Muyiwa Oladoja

Published in American Journal of Theoretical and Applied Statistics (Volume 13, Issue 5)

Received: 24 September 2024 Accepted: 15 October 2024 Published: 31 October 2024

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Abstract

Background: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. Objective: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. Method: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. Result: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. Conclusion: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.

Published in	American Journal of Theoretical and Applied Statistics (Volume 13, Issue 5)
DOI	10.11648/j.ajtas.20241305.16
Page(s)	175-180
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

Fractal Theory, Scaling Principle, Levy Model, Price Changes

References

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APA Style

Abimbola, L. A., Adegoke, T. M., Oladoja, O. M. (2024). Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. American Journal of Theoretical and Applied Statistics, 13(5), 175-180. https://doi.org/10.11648/j.ajtas.20241305.16

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ACS Style

Abimbola, L. A.; Adegoke, T. M.; Oladoja, O. M. Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. Am. J. Theor. Appl. Stat. 2024, 13(5), 175-180. doi: 10.11648/j.ajtas.20241305.16

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AMA Style

Abimbola LA, Adegoke TM, Oladoja OM. Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. Am J Theor Appl Stat. 2024;13(5):175-180. doi: 10.11648/j.ajtas.20241305.16

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@article{10.11648/j.ajtas.20241305.16,
  author = {Latifat Adebisi Abimbola and Taiwo Mobolaji Adegoke and Oladapo Muyiwa Oladoja},
  title = {Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {5},
  pages = {175-180},
  doi = {10.11648/j.ajtas.20241305.16},
  url = {https://doi.org/10.11648/j.ajtas.20241305.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241305.16},
  abstract = {Background: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. Objective: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. Method: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. Result: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. Conclusion: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.},
 year = {2024}
}

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TY  - JOUR
T1  - Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics
AU  - Latifat Adebisi Abimbola
AU  - Taiwo Mobolaji Adegoke
AU  - Oladapo Muyiwa Oladoja
Y1  - 2024/10/31
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241305.16
DO  - 10.11648/j.ajtas.20241305.16
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  - 175
EP  - 180
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241305.16
AB  - Background: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. Objective: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. Method: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. Result: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. Conclusion: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.
VL  - 13
IS  - 5
ER  -

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Author Information

Latifat Adebisi Abimbola

Department of Mathematics and Statistics, Abiola Ajimobi Technical University, Ibadan, Nigeria

Contact Email

http://orcid.org/0009-0000-2924-8235
Taiwo Mobolaji Adegoke

The Biotechnology Center, University of Yaounde, Yaounde, Cameroon

Contact Email

http://orcid.org/0000-0003-2507-4973
Oladapo Muyiwa Oladoja

Department of Mathematics and Statistics, Abiola Ajimobi Technical University, Ibadan, Nigeria

Contact Email

http://orcid.org/0000-0002-0766-2248

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APA Style

Abimbola, L. A., Adegoke, T. M., Oladoja, O. M. (2024). Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. American Journal of Theoretical and Applied Statistics, 13(5), 175-180. https://doi.org/10.11648/j.ajtas.20241305.16

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ACS Style

Abimbola, L. A.; Adegoke, T. M.; Oladoja, O. M. Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. Am. J. Theor. Appl. Stat. 2024, 13(5), 175-180. doi: 10.11648/j.ajtas.20241305.16

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AMA Style

Abimbola LA, Adegoke TM, Oladoja OM. Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics. Am J Theor Appl Stat. 2024;13(5):175-180. doi: 10.11648/j.ajtas.20241305.16

Copy | Download

@article{10.11648/j.ajtas.20241305.16,
  author = {Latifat Adebisi Abimbola and Taiwo Mobolaji Adegoke and Oladapo Muyiwa Oladoja},
  title = {Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {13},
  number = {5},
  pages = {175-180},
  doi = {10.11648/j.ajtas.20241305.16},
  url = {https://doi.org/10.11648/j.ajtas.20241305.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241305.16},
  abstract = {Background: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. Objective: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. Method: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. Result: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. Conclusion: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Applying Fractal Theory: Solving the Geometric Challenge of Price Change and Scaling in Economics
AU  - Latifat Adebisi Abimbola
AU  - Taiwo Mobolaji Adegoke
AU  - Oladapo Muyiwa Oladoja
Y1  - 2024/10/31
PY  - 2024
N1  - https://doi.org/10.11648/j.ajtas.20241305.16
DO  - 10.11648/j.ajtas.20241305.16
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  - 175
EP  - 180
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20241305.16
AB  - Background: Price changes in economics present significant geometric challenges due to sharp discontinuities, which cannot be efficiently described by continuous processes like Brownian motion. Traditional models often rely on linear assumptions, yet financial data frequently exhibit irregular, complex patterns. Fractal theory, a mathematical framework, offers a more accurate way to describe these fluctuations by revealing the underlying self-similar structures in price changes and scaling phenomena. This study explores the use of fractal geometry to gain deeper insights into market behavior. Objective: The objective is to demonstrate that an alternative model, constructed based on geometric scaling assumptions, offers a more accurate description of price changes in competitive markets. Method: The study combined the scaling principle from fractal geometry with a stable Levy model to formulate an integrated model. The logarithmic transformation of the model was applied over successive price changes to observe the behavior of market prices. Result: The scaling principle asserts that no specific time interval (such as a day or a week) holds inherent significance in competitive markets. Instead, these time features are compensated or arbitrated away, supporting the idea that market behavior is self-similar across different time scales. Conclusion: The scaling principle provides a more reliable framework for modeling price changes and is recommended for consideration in economic analyses.
VL  - 13
IS  - 5
ER  -

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