IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v29y2013i1p88-99.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
  • Handle: RePEc:eee:intfor:v:29:y:2013:i:1:p:88-99
    DOI: 10.1016/j.ijforecast.2012.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169207012000830
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gonçalves, Sílvia & Meddahi, Nour, 2011. "Box-Cox transforms for realized volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 129-144, January.
    2. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    3. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    4. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, vol. 42(3), pages 619-638, June.
    5. Clements, Michael P. & Hendry, David F., 1997. "An empirical study of seasonal unit roots in forecasting," International Journal of Forecasting, Elsevier, vol. 13(3), pages 341-355, September.
    6. 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.
    7. Bårdsen, Gunnar & Lütkepohl, Helmut, 2011. "Forecasting levels of log variables in vector autoregressions," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1108-1115, October.
    8. Freeman, Jade & Modarres, Reza, 2006. "Inverse Box-Cox: The power-normal distribution," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 764-772, April.
    9. Collins, Sean, 1991. "Prediction Techniques for Box-Cox Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 267-277, July.
    10. Luetkepohl Helmut & Xu Fang, 2011. "Forecasting Annual Inflation with Seasonal Monthly Data: Using Levels versus Logs of the Underlying Price Index," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-23, February.
    11. Sean Collins, 1991. "Prediction techniques for Box-Cox regression models," Finance and Economics Discussion Series 148, Board of Governors of the Federal Reserve System (U.S.).
    12. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    13. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    14. Francis X. Diebold & Lutz Kilian, 2001. "Measuring predictability: theory and macroeconomic applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 657-669.
    15. Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 47-69, January.
    16. Perry Sadorsky & Michael D. McKenzie, 2008. "Power transformation models and volatility forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 587-606.
    17. Nelson, Harold Jr. & Granger, C. W. J., 1979. "Experience with using the Box-Cox transformation when forecasting economic time series," Journal of Econometrics, Elsevier, vol. 10(1), pages 57-69, April.
    18. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    19. Osborn, Denise R. & Heravi, Saeed & Birchenhall, C. R., 1999. "Seasonal unit roots and forecasts of two-digit European industrial production," International Journal of Forecasting, Elsevier, vol. 15(1), pages 27-47, February.
    20. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
    21. Paul De Bruin & Philip Hans Franses, 1999. "Forecasting power-transformed time series data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 807-815.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    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. Mayr, Johannes & Ulbricht, Dirk, 2015. "Log versus level in VAR forecasting: 42 million empirical answers—Expect the unexpected," Economics Letters, Elsevier, vol. 126(C), pages 40-42.
    4. Santiago Cajiao Raigosa & Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Pronósticos para una economía menos volátil: el caso colombiano," COYUNTURA ECONÓMICA, FEDESARROLLO, December.
    5. Nick Taylor, 2016. "Realised Variance Forecasting Under Box-Cox Transformations," Bristol Accounting and Finance Discussion Papers 16/4, School of Economics, Finance, and Management, University of Bristol, UK.
    6. Francesco Audrino & Simon D. Knaus, 2016. "Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1485-1521, December.
    7. repec:eee:intfor:v:33:y:2017:i:4:p:770-785 is not listed on IDEAS
    8. Mihaela SIMIONESCU, 2015. "The Accuracy Of Exchange Rate Forecasts In Romania," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 4(1), pages 54-64, JULY.

    More about this item

    Keywords

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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:intfor:v:29:y:2013:i:1:p:88-99. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.