The Distribution of the Inverse Square Root Transformed Error Component of the Multiplicative Time Series Model
The probability density function, mean and variance of the inverse square-root transformed left-truncated N(1,σ2) error component e*t(=1/ √et) of the multiplicative time series model were established. A comparison of key-statistical properties of e*t and et confirmed normality with mean 1 but with Var(e*t) ≈1/4Var(et) when σ≤0.14. Hence σ≤0.14 is the required condition for successful transformation.
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