Abstract
This paper examines the inverse cube transformation of error component of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the was mathematically proved as a proper pdf since The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.
Highlights
The cube ( ) transformation is a fairly strong transformation with a substantial effect on distribution shape. It is used for reducing right skewness, and has the advantage that it can be applied to zero and non negative values
A similar property is possessed by any other root whose power is the inverse of an odd positive integer example 1/3, 1/5, 1/7, etc
The cubic transformation is stronger than the square transformation, though weaker than the logarithm transformation
Summary
The cube ( ) transformation is a fairly strong transformation with a substantial effect on distribution shape. It is used for reducing right skewness, and has the advantage that it can be applied to zero and non negative values. A similar property is possessed by any other root whose power is the inverse of an odd positive integer example 1/3, 1/5, 1/7, etc. The descriptive time series model is given as:. Where is the secular Trend, is the Seasonal variations, is the Cyclical variation and is the irregular varions or error component. In short term series the trend and cyclical components are merged to give the trend-cycle component; equation (1) can be rewritten as (2)
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