Tommaso, Proietti and Helmut, Luetkepohl (2011): Does the BoxCox transformation help in forecasting macroeconomic time series?

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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 BoxCox 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 BoxCox transformation produces forecasts significantly better than the untransformed data at onestepahead 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¨ıve 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 insample frequency domain assessment conducted provides a reliable guidance which series should be transformed for improving significantly the predictive performance.
Item Type:  MPRA Paper 

Original Title:  Does the BoxCox transformation help in forecasting macroeconomic time series? 
Language:  English 
Keywords:  Forecasts comparisons; Multistep forecasting; Rolling forecasts; Nonparametric estimation of prediction error variance. 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  32294 
Depositing User:  Tommaso Proietti 
Date Deposited:  18. Jul 2011 12:27 
Last Modified:  11. Mar 2015 15:11 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/32294 