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Forecasting levels of log variables in vector autoregressions

  • Bårdsen, Gunnar
  • Lütkepohl, Helmut

Sometimes forecasts of the original variable are of interest, even though 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 naïve forecast of the original variable by simply applying the exponential transformation is not theoretically optimal. A simple expression for the optimal forecast under normality assumptions is derived. However, despite its theoretical advantages, the optimal forecast is shown to be inferior to the naïve 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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Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 27 (2011)
Issue (Month): 4 (October)
Pages: 1108-1115

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Handle: RePEc:eee:intfor:v:27:y:2011:i:4:p:1108-1115
Contact details of provider: Web page: http://www.elsevier.com/locate/ijforecast

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  1. 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.
  2. Helmut Luetkepohl & Fang Xu, 2009. "The Role of the Log Transformation in Forecasting Economic Variables," CESifo Working Paper Series 2591, CESifo Group Munich.
  3. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
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