Forecasting Levels of log Variables in Vector Autoregressions

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Forecasting Levels of log Variables in Vector Autoregressions

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Gunnar Bardsen
Helmut Luetkepohl

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Abstract

Sometimes forecasts of the original variable are of interest although a variable appears in logarithms (logs) in a system of time series. In that case converting the forecast for the log of the variable to a naive forecast of the original variable by simply applying the exponential transformation is not optimal theoretically. A simple expression for the optimal forecast under normality assumptions is derived. Despite its theoretical advantages the optimal forecast is shown to be inferior to the naive forecast if specification and estimation uncertainty are taken into account. Hence, in practice using the exponential of the log forecast is preferable to using the optimal forecast.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2009/24.

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Date of creation: 2009
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Handle: RePEc:eui:euiwps:eco2009/24

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Paper
- 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. [Downloadable!]

Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2009-07-11 (All new papers)
NEP-CBA-2009-07-11 (Central Banking)
NEP-ECM-2009-07-11 (Econometrics)
NEP-FOR-2009-07-11 (Forecasting)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!] (restricted)

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