Selection of the optimal Box-Cox transformation parameter for modelling and forecasting age-specific fertility

TL;DR

This paper proposes a simple method for selecting the optimal Box-Cox transformation parameter to improve the modeling and forecasting of age-specific fertility, demonstrating enhanced accuracy over traditional log transformation methods.

Contribution

It introduces an algorithm for optimal Box-Cox parameter selection in demographic forecasting, emphasizing its importance over the standard log transformation.

Findings

Optimal Box-Cox parameter improves forecast accuracy

Log transformation is inadequate for age-specific fertility modeling

Embedding Box-Cox in analysis captures forecast uncertainties

Abstract

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.