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Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?

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  • Tommaso Proietti
  • Helmut Luetkepohl

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 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.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2011/29.

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Date of creation: 2011
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Handle: RePEc:eui:euiwps:eco2011/29

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Keywords: Forecasts comparisons. Multi-step forecasting. Rolling forecasts. Nonparametric estimation of prediction error variance.;

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References

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  1. Sean Collins, 1991. "Prediction techniques for Box-Cox regression models," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 148, Board of Governors of the Federal Reserve System (U.S.).
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Cited by:
  1. Audrino, Francesco & Knaus, Simon, 2012. "Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics," Economics Working Paper Series 1224, University of St. Gallen, School of Economics and Political Science.
  2. Hector Manuel Zárate Solano & Angélica Rengifo Gómez, 2013. "Forecasting annual inflation with power transformations: the case of inflation targeting countries," Borradores de Economia 756, Banco de la Republica de Colombia.
  3. Weigand, Roland, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," University of Regensburg Working Papers in Business, Economics and Management Information Systems 478, University of Regensburg, Department of Economics.
  4. Santiago Cajiao Raigosa & Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Pronósticos para una economía menos volátil: El caso colombiano," BORRADORES DE ECONOMIA 011252, BANCO DE LA REPÚBLICA.
  5. Héctor Manuel Záarte Solano & Angélica Rengifo Gómez, 2013. "Forecasting annual inflation with power transformations: the case of inflation targeting countries," BORRADORES DE ECONOMIA 010462, BANCO DE LA REPÚBLICA.

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