The Distribution of the Inverse Square Root Transformed Error Component of the Multiplicative Time Series Model

Authors

Bright F. Ajibade, Petroleum Training Institute, NigeriaFollow
Chinwe R. Nwosu, Nnamdi Azikiwe University, Nigeria
J. I. Mbegdu, University of Benin, Nigeria

Abstract

The probability density function, mean and variance of the inverse square-root transformed left-truncated N(1,σ²) error component e^*_t(=1/ √e_t) of the multiplicative time series model were established. A comparison of key-statistical properties of e^*_t and e_t confirmed normality with mean 1 but with Var(e^*_t) ≈1/4Var(e_t) when σ≤0.14. Hence σ≤0.14 is the required condition for successful transformation.

DOI

10.22237/jmasm/1446351240