Condition for Successful Square Transformation in Time Series Modeling
- 1 Department of Statistics, Faculty of Science, Federal University Otuoke, Yenagoa, Nigeria
- 2 Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, Uturu, Nigeria
- 3 Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, Uturu, Nigeria
Abstract
In this study we establish the probability density function of the square transformed left-truncated N (1, σ 2 ) error com ponent of the multiplicative time series model and the functional expressions for its mean and variance. Furthermore the mean and variance of the square transformed left-truncated N (1, σ 2 ) error component and those of the untransformed component were compared for the purpose of establishing the interval for σ where the properties of the two distributions are approximately the same in terms of equality of means and normality. From the results of the study, it was established that the two distributions are normally distributed and have means ≌ 1.0 correct to 1 dp in the interval 0 < σ < 0.027 , hence a successful square transformation where necessary is achieved for values of σ such that 0 < σ < 0.027 .
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