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The Role of the Log Transformation in Forecasting Economic Variables

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  • Helmut Luetkepohl
  • Fang Xu

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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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2591.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2591

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Keywords: autoregressive moving average process; forecast mean squared error; instantaneous transformation; integrated process; heteroskedasticity;

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  1. Andrea Silvestrini & Matteo Salto & Laurent Moulin & David Veredas, 2008. "Monitoring and forecasting annual public deficit every month: the case of France," Empirical Economics, Springer, vol. 34(3), pages 493-524, June.
  2. 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.
  3. Markku Lanne, Helmut Luetkepohl, 2006. "Identifying Monetary Policy Shocks via Changes in Volatility," Economics Working Papers ECO2006/23, European University Institute.
  4. Christopher A. Sims & Daniel F. Waggoner & Tao Zha, 2006. "Methods for inference in large multiple-equation Markov-switching models," Working Paper 2006-22, Federal Reserve Bank of Atlanta.
  5. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  6. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta.
  7. Arino, Miguel A. & Franses, Philip Hans, 2000. "Forecasting the levels of vector autoregressive log-transformed time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 111-116.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Log Transformations & Forecasting
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-22 19:20:00
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Cited by:
  1. Roxana Halbleib & Valeri Voev, 2012. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Paper Series of the Department of Economics, University of Konstanz 2012-30, Department of Economics, University of Konstanz.
  2. Gunnar Bårdsen and Helmut Lütkepohl, 2009. "Forecasting Levels of log Variables in Vector Autoregressions," Working Paper Series 10409, Department of Economics, Norwegian University of Science and Technology.
  3. Rossen, Anja, 2011. "On the predictive content of nonlinear transformations of lagged autoregression residuals and time series observations," HWWI Research Papers 113, Hamburg Institute of International Economics (HWWI).
  4. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing,CIRET, vol. 2010(2), pages 1-26.
  5. 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.

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