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

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.