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\na large set of seasonal monthly macroeconomic time series related to industrial production and retail turnover. In about one fifth of the series considered the Box-Cox transformation produces forecasts significantly better than the untransformed data at one-step-ahead horizon; in most of\nthe 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 na¨ıve predictor that just reverses the transformation leads to a lower mean square error than the optimal\npredictor at short forecast leads. We also discuss whether the preliminary in-sample frequency domain assessment conducted provides a reliable guidance which series should be transformed for improving significantly the predictive performance.
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