On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation

Chris Uchechi Onyemachi; Sidney Ifeanyi Onyeagu; Samuel Ademola Phillips; Jamiu Adebowale Oke; Callistus Ezekwe Ugwo

doi:doi:10.11648/j.ijdsa.20210704.12

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On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation

Chris Uchechi Onyemachi, Sidney Ifeanyi Onyeagu, Samuel Ademola Phillips, Jamiu Adebowale Oke, Callistus Ezekwe Ugwo

Published in International Journal of Data Science and Analysis (Volume 7, Issue 4)

Received: 9 September 2021 Accepted: 28 September 2021 Published: 12 October 2021

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Abstract

We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.

Published in	International Journal of Data Science and Analysis (Volume 7, Issue 4)
DOI	10.11648/j.ijdsa.20210704.12
Page(s)	109-116
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), 2021. Published by Science Publishing Group

Keywords

Multiplicative Error Model, Error Component, Weibull Distribution, Inverse Square Root Transformation, Remedial Measure

References

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[5]	Engle R. F and Russell J. R. (1998). Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data, Econometrica, Vol. 66, issue 5, 1127-1162.
[6]	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.
[7]	Engle, R. F. (2002). Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models, Journal of Business & Economic Statistics, 20, 339-350. https://doi.org/10.1198/073500102288618487.
[8]	Horst, R (2008). Related distributions from: The Weibull Distribution, A handbook CRC Presss. Accessed on: 12 Jul 2019. https://www.routledgehandbooks.com/doi/10.1201/9781420087444.ch3.
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[12]	Nwosu, C. R, Iwueze, I. S, Ohakwe, J (2013). Condition for successful inverse transformation of the error component of the multiplicative time series model. Asian Journal of Applied Sciences,: 6 (1): 1–15. DOI: 10.3923/ajaps.2013. 1-15.
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[16]	Ohakwe, J. (2013). The Effect of Inverse Transformation on the Unit Mean and Constant Variance Assumptions of a Multiplicative Error Model whose error Component has a Gamma Distribution. Math’l Modeling Vol. 3, No. 3 pp 44-52.
[17]	Okorie, I. E., Akpanta, A. C., Ohakwe, J., and Chikezie, D. C. (2017). The Adjusted Fisk Weibull Distribution: Properties and Applications. International Journal of Modeling and Simulation https://doi.org/10.1080/02286203.2017.1370770.
[18]	Onyemachi, C. U. (2021). Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Model. Science Journal of Applied Mathematics and Statistics. Vol. 9, No. 4, 2021, pp. 94-105.
[19]	Otuonye, E. L., Iwueze, I. S and Ohakwe, J. (2011). The effect of square root transformation on the error component of the multiplicative time series model. International Journal of Statistics and Systems. Vol. 6, No. 4 pp 461-476.
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APA Style

Chris Uchechi Onyemachi, Sidney Ifeanyi Onyeagu, Samuel Ademola Phillips, Jamiu Adebowale Oke, Callistus Ezekwe Ugwo. (2021). On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. International Journal of Data Science and Analysis, 7(4), 109-116. https://doi.org/10.11648/j.ijdsa.20210704.12

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ACS Style

Chris Uchechi Onyemachi; Sidney Ifeanyi Onyeagu; Samuel Ademola Phillips; Jamiu Adebowale Oke; Callistus Ezekwe Ugwo. On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. Int. J. Data Sci. Anal. 2021, 7(4), 109-116. doi: 10.11648/j.ijdsa.20210704.12

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AMA Style

Chris Uchechi Onyemachi, Sidney Ifeanyi Onyeagu, Samuel Ademola Phillips, Jamiu Adebowale Oke, Callistus Ezekwe Ugwo. On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. Int J Data Sci Anal. 2021;7(4):109-116. doi: 10.11648/j.ijdsa.20210704.12

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@article{10.11648/j.ijdsa.20210704.12,
  author = {Chris Uchechi Onyemachi and Sidney Ifeanyi Onyeagu and Samuel Ademola Phillips and Jamiu Adebowale Oke and Callistus Ezekwe Ugwo},
  title = {On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation},
  journal = {International Journal of Data Science and Analysis},
  volume = {7},
  number = {4},
  pages = {109-116},
  doi = {10.11648/j.ijdsa.20210704.12},
  url = {https://doi.org/10.11648/j.ijdsa.20210704.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20210704.12},
  abstract = {We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.},
 year = {2021}
}

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TY  - JOUR
T1  - On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation
AU  - Chris Uchechi Onyemachi
AU  - Sidney Ifeanyi Onyeagu
AU  - Samuel Ademola Phillips
AU  - Jamiu Adebowale Oke
AU  - Callistus Ezekwe Ugwo
Y1  - 2021/10/12
PY  - 2021
N1  - https://doi.org/10.11648/j.ijdsa.20210704.12
DO  - 10.11648/j.ijdsa.20210704.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 109
EP  - 116
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20210704.12
AB  - We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.
VL  - 7
IS  - 4
ER  -

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Author Information

Chris Uchechi Onyemachi

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
Sidney Ifeanyi Onyeagu

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
Samuel Ademola Phillips

Department of Statistics, Federal School of Statistics, School of Sciences, Ibadan, Nigeria
Jamiu Adebowale Oke

Department of Statistics, Federal School of Statistics, School of Sciences, Ibadan, Nigeria
Callistus Ezekwe Ugwo

Department of Statistics, Federal School of Statistics, School of Sciences, Enugu, Nigeria

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Plain Text BibTeX RIS

APA Style

Chris Uchechi Onyemachi, Sidney Ifeanyi Onyeagu, Samuel Ademola Phillips, Jamiu Adebowale Oke, Callistus Ezekwe Ugwo. (2021). On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. International Journal of Data Science and Analysis, 7(4), 109-116. https://doi.org/10.11648/j.ijdsa.20210704.12

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ACS Style

Chris Uchechi Onyemachi; Sidney Ifeanyi Onyeagu; Samuel Ademola Phillips; Jamiu Adebowale Oke; Callistus Ezekwe Ugwo. On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. Int. J. Data Sci. Anal. 2021, 7(4), 109-116. doi: 10.11648/j.ijdsa.20210704.12

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AMA Style

Chris Uchechi Onyemachi, Sidney Ifeanyi Onyeagu, Samuel Ademola Phillips, Jamiu Adebowale Oke, Callistus Ezekwe Ugwo. On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation. Int J Data Sci Anal. 2021;7(4):109-116. doi: 10.11648/j.ijdsa.20210704.12

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@article{10.11648/j.ijdsa.20210704.12,
  author = {Chris Uchechi Onyemachi and Sidney Ifeanyi Onyeagu and Samuel Ademola Phillips and Jamiu Adebowale Oke and Callistus Ezekwe Ugwo},
  title = {On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation},
  journal = {International Journal of Data Science and Analysis},
  volume = {7},
  number = {4},
  pages = {109-116},
  doi = {10.11648/j.ijdsa.20210704.12},
  url = {https://doi.org/10.11648/j.ijdsa.20210704.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20210704.12},
  abstract = {We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.},
 year = {2021}
}

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TY  - JOUR
T1  - On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation
AU  - Chris Uchechi Onyemachi
AU  - Sidney Ifeanyi Onyeagu
AU  - Samuel Ademola Phillips
AU  - Jamiu Adebowale Oke
AU  - Callistus Ezekwe Ugwo
Y1  - 2021/10/12
PY  - 2021
N1  - https://doi.org/10.11648/j.ijdsa.20210704.12
DO  - 10.11648/j.ijdsa.20210704.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 109
EP  - 116
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20210704.12
AB  - We first consider the Multiplicative Error Model (MEM) introduced in financial econometrics by Engle (2002) as a general class of time series model for positive-valued random variables, which are decomposed into the product of their conditional mean and a positive-valued error term. Considering the possibility that the error component of a MEM can be a Weibull distribution and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the inverse square root transformation (ISRT) on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of the Weibull distribution and those of the inverse square root transformed distribution are calculated for σ=6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The paper concludes that the inverse square root would yield better results when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.
VL  - 7
IS  - 4
ER  -

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