SOURCE:

Faculty: Physical Sciences
Department: Statistics

CONTRIBUTORS:

Ajibade, F.B;
Ogum, F.E.O;
Mbegbu, J.I;

ABSTRACT:

In this study, the distribution and properties of the left-truncated N(1,σ^2 ) error term, e_t, of the multiplicative time series model under inverse-square-root transformation was investigated with a view to establish the condition for the transformed error term, e_t^*, to be normally distributed with mean, 1. The curve shapes of the probability density function of e_t^*; g(y) for different values of standard deviation σ, σ∈[0.01,0.5], and by the Rolle’s theorem showed that g(y) is bell-shaped with mode ≈ 1 when σ ≤0.15. Furthermore, the normality of e_t^* is attained forσ<0.15 and the functional forms of and confirmed the mean of e_t^* to be 1 with , whenever σ ≤0.15 Hence σ ≤0.15 is the recommended condition for successful inverse square root transformation.