In this paper, the probability density function (pdf), of the cube root transformation was derived from the 𝐧𝐧𝐭𝐭𝐭𝐭 power transformation of the error component of the multiplicative time series model. The mean and variance of the cube root transformation were equally established. From the simulated results it was found that the cube root transformed error component was normal with unit mean and variance approximately 𝟏𝟏 𝟗𝟗 times that of the original error before transformation. Furthermore, the Kolmogorov-Smirnov test for normality was used ascertain the effect of cube root transformation as regard to normalization, from the results of the test at p-value of 0.05, we accepted normality for σ values of 0.001 to 0.22. Hence, a successful transformation is achieved when 𝟎𝟎 ≤ 𝛔𝛔 ≤ 𝟎𝟎. 𝟐𝟐𝟐𝟐 depending on the decimal places desired.