  The Box-Cox transformation can sometimes yield noticeable improvements in
model simplicity, variance homogeneity and precision of estimation, such as in
modelling and forecasting age-specific fertility. Despite its importance, there
have been few studies focusing on the optimal selection of Box-Cox
transformation parameters in demographic forecasting. A simple method is
proposed for selecting the optimal Box-Cox transformation parameter, along with
an algorithm based on an in-sample forecast error measure. Illustrated by
Australian age-specific fertility, the out-of-sample accuracy of a forecasting
method can be improved with the selected Box-Cox transformation parameter.
Furthermore, the log transformation is not adequate for modelling and
forecasting age-specific fertility. The Box-Cox transformation parameter should
be embedded in statistical analysis of age-specific demographic data, in order
to fully capture forecast uncertainties.
