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

  • Lütkepohl, Helmut
  • Proietti, Tommaso

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 naïve 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.

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File URL: http://hdl.handle.net/2123/8167
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Paper provided by University of Sydney Business School, Discipline of Business Analytics in its series Working Papers with number 1 OMEWP.

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Date of creation: Oct 2011
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Handle: RePEc:syb:wpbsba:2123/8167
Contact details of provider: Phone: +61 2 9351 8083
Web page: http://sydney.edu.au/business/business_analytics
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