Archive Volume 7 , Issue 4 , August 2021 , Pages: 109 - 116
On a Weibull-Distributed Error Component of a Multiplicative Error Model Under Inverse Square Root Transformation
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
Received: Sep. 9, 2021;       Accepted: Sep. 28, 2021;       Published: Oct. 12, 2021
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.
Keywords
Multiplicative Error Model, Error Component, Weibull Distribution, Inverse Square Root Transformation, Remedial Measure
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, International Journal of Data Science and Analysis. Vol. 7, No. 4, 2021, pp. 109-116. doi: 10.11648/j.ijdsa.20210704.12
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