This paper provides the building block for transformations to be carried out in the additive time series model. The probability density function of the exponentially transformed random series of the additive time series model was derived. The mean and variance were established and shown to be and respectively. The condition for the mean of the original series = 0 while that of the truncated series = 1 was shown to be 0 < σ ≤ 0.31 to one decimal place. The variance of the original series and the exponentially transformed series are equal for 0 < σ < 0.35 to one decimal place. truncated series was tested for normality and it showed that for σ ≤ 0.13 it was normally distributed. The theoretical mean and variance of the original series and the truncated series was confirmed with the simulation carried out for σ ≤ 0.13
Keywords: Additive Time series Model, Error component, Exponential transformation., Probability density function
