Exact Box-Cox Analysis

The Box-Cox method has been widely used to improve estimation accuracy in different fields, especially in econometrics and time series. In this thesis, we initially review the Box-Cox transformation [Box and Cox, 1964] and other alternative parametric power transformations. Following, the maximum likelihood method for the Box-Cox transformation is presented by discussing the problems of previous approaches in the literature. This work consists of the exact analysis of Box-Cox transformation taking into account the truncation effect in the transformed domain. We introduce a new family of distributions for the Box-Cox transformation in the original and transformed data scales. A likelihood analysis of the Box-Cox distribution is presented when truncation is considered. It is shown that numerical problems may arise in prediction and simulation when the truncation effect is ignored. A new algorithm has been developed for simulating Box-Cox transformed time series since previous methods are inefficient or unreliable. An application to sunspot data is discussed. Box-Cox analysis is employed for random forest regression prediction using cross-validation instead of MLE to estimate the transformation. An application to Boston housing dataset demonstrates that this technique can substantially improve prediction accuracy