Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model

Onyemachi Chris Uchechi

doi:doi:10.11648/j.sjams.20210904.11

| Peer-Reviewed

Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model

Onyemachi Chris Uchechi

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 4)

Received: 8 July 2021 Accepted: 19 July 2021 Published: 27 July 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) 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 square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions 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 fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance 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	Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 4)
DOI	10.11648/j.sjams.20210904.11
Page(s)	94-105
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

Multiplicative Error Model, Weibull Distribution, Square Transformation, Mean, Variance

References

[1]	Anderson, D. R. (2008). Model Based Inference in the Life Sciences: A Primer on Evidence. Springer New York.
[2]	Akpanta, A. C and Iwueze, I. S. (2009). On applying the Barlett transformation methods to time series data. Journal of Math’l Sciences. Vol. 20 No. 3 pp 227 – 243.
[3]	Bandi, F. M. and Russell, J. R. (2006). Separating microstructure noise from volatility. Journal of Financial Economics, 79, 655-692.
[4]	Brownlees C. T, Cipollini F., and Gallo G. M. (2011). Multiplicative Error Models. Working paper. http:ssrn.com/abstract=1852285.
[5]	Chatfield, C. (2004). The Analysis of time Series: An introduction 6^th ed. Chapman and Hall. CRC Press. Boca Raton.
[6]	Dike, A. O., Otuonye, E. L and Chikezie, D. C. (2016). The nth Power Transformation of the Error Component of the Multiplicative Time Series Model. British Journal of Mathematics & Computer Science, 18 (1), 1-15 DOI: 10.1186/1471-2334-11-218.
[7]	Engle, R. (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]	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.
[9]	Iwu, H., Iwueze, I. S and Nwogu, E. C. (2009). Trend Analysis of Transformations of the Multiplicative Time Series Model. Journal of Nigerian Statistical Association 21, 40-54.
[10]	Iwueze I. S (2007). Some Implications of Truncating the N (1,σ²) Distribution to the left at Zero. JASA, Vol 7 (2), 189 – 195.
[11]	Iwueze, I. S., Akpanta, A. C. and Iwu, H. C (2008). Seasonal Analysis of Transformations of the Multiplicative Time Series Model. Asian J. Math. Statist., 1: 80=89.
[12]	Manganelli, S. (2005). Duration, Volume and Volatility Impact of Trades". Journal of Financial Markets 8, pp. 377-399.
[13]	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.
[14]	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.
[15]	Ozdemir O. (2017). Power transformations for families of statistical distributions to satisfy normality. International Journal of Economics and Statistics, Vol. 5, pp. 1 – 4.
[16]	Ramachandran K. M. And Tsokos C. P (2009). Mathematical Statistics with Applications, pp. 156 – 159. Published by Academic Press, an imprint of Elsevier. ISBN: 13: 978-0-12-374848-5.
[17]	Russell, J. R. and R. F. Engle (2010). Analysis of high-frequency data. In Ait-Sahalia, Y. and L. P. Hansen, (eds) Handbook of Financial Econometrics, Volume 1 Tools and Techniques, 383-427. Amsterdam: North Holland Publishing. Society. B. Vol. 26 pp 211 – 243.
[18]	Tsay, R (2007). Handbook in Econometrics II Palgrave Publishing Company. NY.

Cite This Article

Plain Text BibTeX RIS

APA Style

Onyemachi Chris Uchechi. (2021). Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Science Journal of Applied Mathematics and Statistics, 9(4), 94-105. https://doi.org/10.11648/j.sjams.20210904.11

Copy | Download

ACS Style

Onyemachi Chris Uchechi. Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Sci. J. Appl. Math. Stat. 2021, 9(4), 94-105. doi: 10.11648/j.sjams.20210904.11

Copy | Download

AMA Style

Onyemachi Chris Uchechi. Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Sci J Appl Math Stat. 2021;9(4):94-105. doi: 10.11648/j.sjams.20210904.11

Copy | Download

@article{10.11648/j.sjams.20210904.11,
  author = {Onyemachi Chris Uchechi},
  title = {Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {4},
  pages = {94-105},
  doi = {10.11648/j.sjams.20210904.11},
  url = {https://doi.org/10.11648/j.sjams.20210904.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210904.11},
  abstract = {This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) 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 square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions 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 fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance 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}
}

Copy | Download

TY  - JOUR
T1  - Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model
AU  - Onyemachi Chris Uchechi
Y1  - 2021/07/27
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210904.11
DO  - 10.11648/j.sjams.20210904.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 94
EP  - 105
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210904.11
AB  - This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) 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 square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions 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 fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance 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  - 9
IS  - 4
ER  -

Copy | Download

Author Information

Onyemachi Chris Uchechi

Department of Statistics, Faculty of Physical Sciences, Abia State University, Uturu, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Onyemachi Chris Uchechi. (2021). Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Science Journal of Applied Mathematics and Statistics, 9(4), 94-105. https://doi.org/10.11648/j.sjams.20210904.11

Copy | Download

ACS Style

Onyemachi Chris Uchechi. Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Sci. J. Appl. Math. Stat. 2021, 9(4), 94-105. doi: 10.11648/j.sjams.20210904.11

Copy | Download

AMA Style

Onyemachi Chris Uchechi. Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model. Sci J Appl Math Stat. 2021;9(4):94-105. doi: 10.11648/j.sjams.20210904.11

Copy | Download

@article{10.11648/j.sjams.20210904.11,
  author = {Onyemachi Chris Uchechi},
  title = {Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {4},
  pages = {94-105},
  doi = {10.11648/j.sjams.20210904.11},
  url = {https://doi.org/10.11648/j.sjams.20210904.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210904.11},
  abstract = {This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) 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 square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions 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 fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance 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}
}

Copy | Download

TY  - JOUR
T1  - Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model
AU  - Onyemachi Chris Uchechi
Y1  - 2021/07/27
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210904.11
DO  - 10.11648/j.sjams.20210904.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 94
EP  - 105
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210904.11
AB  - This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) 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 square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions 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 fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance 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  - 9
IS  - 4
ER  -

Copy | Download