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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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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. Franses, Philip Hans & Koop, Gary, 1998. "On the sensitivity of unit root inference to nonlinear data transformations," Economics Letters, Elsevier, vol. 59(1), pages 7-15, April.
  2. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
  3. Markku Lanne, Helmut Luetkepohl, 2006. "Identifying Monetary Policy Shocks via Changes in Volatility," Economics Working Papers ECO2006/23, European University Institute.
  4. SILVESTRINI, Andrea & SALTo, Matteo & MOULIN, Laurent & VEREDAS, David, . "Monitoring and forecasting annual public deficit every month: the case of France," CORE Discussion Papers RP -2019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Kramer, Walter & Davies, Laurie, 2002. "Testing for unit roots in the context of misspecified logarithmic random walks," Economics Letters, Elsevier, vol. 74(3), pages 313-319, February.
  6. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  7. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  8. 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.
  9. Valentina Corradi & Norman R. Swanson, 2003. "The Effect of Data Transformation on Common Cycle, Cointegration and Unit Root Tests: Monte Carlo Results and a Simple Test," Departmental Working Papers 200322, Rutgers University, Department of Economics.
  10. Ari�o, M.A. & Franses, Ph.H.B.F., 1996. "Forecasting the Levels of Vector Autoregressive Log-Transformed Time Series," Econometric Institute Research Papers EI 9669-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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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. Gunnar Bardsen & Helmut Luetkepohl, 2009. "Forecasting Levels of log Variables in Vector Autoregressions," Economics Working Papers ECO2009/24, European University Institute.
  2. Tommaso Proietti & Helmut Luetkepohl, 2011. "Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?," Economics Working Papers ECO2011/29, European University Institute.
  3. 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.
  4. Roxana Halbleib & Valeri Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," CREATES Research Papers 2011-03, School of Economics and Management, University of Aarhus.
  5. 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.
  6. 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).
  7. 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.
  8. 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.
  9. 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.

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