Generalized Power Transformation of Error Components of Multiplicative Time Series Model

A. O. Dike; E. L. Otuonye; D. C. Chikezie

A. O. Dike Department of Mathematics and Statistics, Akanu Ibiam Federal Polytechnic, Unwana, P.M.B.1007, Afikpo, Ebonyi State, Nigeria.
E. L. Otuonye Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, P.M.B.2000, Uturu, Nigeria.
D. C. Chikezie Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, P.M.B.2000, Uturu, Nigeria.

Keywords: Power transformations, probability density, function, error component, multiplicative time series, cube root

Abstract

In this paper the author(s) present derivations for the mean and variance of the n^th power transformation of the error component of the multiplicative time series model. As a general rule to any power transformation. Some of the published transformations like the square root and the inverse were used to validate the results obtained. The results showed that they conformed to the general rule, Also the cube transformation equally used to establish a practical illustration of the general rule. Data from federal road safety commission (FRSC) Nigeria on road accident were collected and analyzed by fitting the regression line of log mean (logmean) against log standard deviation (logstdev). This gave a slope which agrees with the required value of 0.6666 this gives a transformation of 1-0.666977= 0.333023 (1- which is the cube root transformation. Data were later decomposed into time series components. Recommendations on areas of application of cube root transformation were equally given.