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

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  • Proietti, Tommaso
  • Lütkepohl, Helmut

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.

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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 29 (2013)
Issue (Month): 1 ()
Pages: 88-99

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Handle: RePEc:eee:intfor:v:29:y:2013:i:1:p:88-99

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Web page: http://www.elsevier.com/locate/ijforecast

Related research

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

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  1. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2005. "Bootstrap prediction intervals for power-transformed time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 219-235.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Santiago Cajiao Raigosa & Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Pronósticos para una economía menos volátil: El caso colombiano," Borradores de Economia 821, Banco de la Republica de Colombia.
  5. 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.
  6. 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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