Type: Working Paper
Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?
Working Paper, EUI ECO, 2011/29
PROIETTI, Tommaso, LUETKEPOHL, Helmut, Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?, EUI ECO, 2011/29 - https://hdl.handle.net/1814/19334
Retrieved from Cadmus, EUI Research Repository
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 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 the 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¨ive predictor that just reverses the transformation leads to a lower mean square error than the optimal predictor 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.
Cadmus permanent link: https://hdl.handle.net/1814/19334
Series/Number: EUI ECO; 2011/29