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The role of the log transformation in forecasting economic variables

Author

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  • Helmut Lütkepohl
  • Fang Xu

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Abstract

For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. It is found that it depends on the data generation process whether the former or the latter are preferable. For a range of economic variables substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:empeco:v:42:y:2012:i:3:p:619-638
    DOI: 10.1007/s00181-010-0440-1
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Festic, Mejra & Kavkler, Alenka & Repina, Sebastijan, 2011. "The macroeconomic sources of systemic risk in the banking sectors of five new EU member states," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 310-322, February.
    4. Ji, In Bae & Chung, Chanjin, 2012. "Causality Between Captive Supplies and Cash Market Prices in the U.S. Cattle Procurement Market," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 41(3), December.
    5. Ioannis Chatziantoniou & Stavros Degiannakis & Bruno Eeckels & George Filis, 2016. "Forecasting tourist arrivals using origin country macroeconomics," Applied Economics, Taylor & Francis Journals, vol. 48(27), pages 2571-2585, June.
    6. Kriechbaumer, Thomas & Angus, Andrew & Parsons, David & Rivas Casado, Monica, 2014. "An improved wavelet–ARIMA approach for forecasting metal prices," Resources Policy, Elsevier, vol. 39(C), pages 32-41.
    7. 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.
    8. Tuhkuri, Joonas, 2016. "Forecasting Unemployment with Google Searches," ETLA Working Papers 35, The Research Institute of the Finnish Economy.
    9. 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.
    10. Rossen Anja, 2016. "On the Predictive Content of Nonlinear Transformations of Lagged Autoregression Residuals and Time Series Observations," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(3), pages 389-409, May.
    11. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    12. Tuhkuri, Joonas, 2016. "ETLAnow: A Model for Forecasting with Big Data – Forecasting Unemployment with Google Searches in Europe," ETLA Reports 54, The Research Institute of the Finnish Economy.
    13. Donal Smith, 2016. "The International Impact of Financial Shocks: A Global VAR and Connectedness Measures Approach," Discussion Papers 16/07, Department of Economics, University of York.
    14. repec:eee:intfor:v:33:y:2017:i:4:p:770-785 is not listed on IDEAS
    15. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
    16. Grosche, Stephanie & Heckelei, Thomas, 2014. "Directional Volatility Spillovers between Agricultural, Crude Oil, Real Estate and other Financial Markets," Discussion Papers 166079, University of Bonn, Institute for Food and Resource Economics.
    17. Radovan Parrák, 2013. "The Economic Valuation of Variance Forecasts: An Artificial Option Market Approach," Working Papers IES 2013/09, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Aug 2013.
    18. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(2), pages 383-417.
    19. Damen, Sven & Vastmans, Frank & Buyst, Erik, 2016. "The effect of mortgage interest deduction and mortgage characteristics on house prices," Journal of Housing Economics, Elsevier, vol. 34(C), pages 15-29.

    More about this item

    Keywords

    Autoregressive moving average process; Forecast mean squared error; Instantaneous transformation; Integrated process; Heteroskedasticity; C22;

    JEL classification:

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

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