The Role of the Log Transformation in Forecasting Economic Variables

32 Pages Posted: 25 Mar 2009

See all articles by Helmut Luetkepohl

Helmut Luetkepohl

European University Institute; CESifo (Center for Economic Studies and Ifo Institute)

Fang Xu

European University Institute; Christian-Albrechts-University of Kiel

Date Written: March 2009

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.

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

JEL Classification: C22

Suggested Citation

Luetkepohl, Helmut and Xu, Fang, The Role of the Log Transformation in Forecasting Economic Variables (March 2009). CESifo Working Paper Series No. 2591, Available at SSRN: https://ssrn.com/abstract=1368131

Helmut Luetkepohl (Contact Author)

European University Institute ( email )

Villa San Paulo
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Italy
+39 055 4685 971 (Phone)
+39 055 4685 902 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

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Munich, DE-81679
Germany

Fang Xu

European University Institute ( email )

Max Weber Programme
Via delle Fontanelle 10,
Florence, Tuscany 50014
Italy

Christian-Albrechts-University of Kiel ( email )

Olshausenstr. 40-60
Kiel, 24118
Germany

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