Does the Box–Cox transformation help in forecasting macroeconomic time series?

Abstract

The paper investigates whether transforming a time series leads to an improvement in forecasting accuracy. The class of transformations that is considered is the Box–Cox power transformation, which applies to series measured on a ratio scale. We propose a nonparametric approach for estimating the optimal transformation parameter based on the frequency domain estimation of the prediction error variance, and also conduct an extensive recursive forecast experiment on a large set of seasonal monthly macroeconomic time series related to industrial production and retail turnover. In about a fifth of the series considered, the Box–Cox transformation produces forecasts which are significantly better than the untransformed data at the one-step-ahead horizon; in most cases, the logarithmic transformation is the relevant one. As the forecast horizon increases, the evidence in favour of a transformation becomes less strong. Typically, the naïve predictor that just reverses the transformation leads to a lower mean square error than the optimal predictor at short forecast lead times. We also discuss whether the preliminary in-sample frequency domain assessment conducted here provides reliable guidance as to which series should be transformed in order to improve the predictive performance significantly.