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Forecasting Levels of log Variables in Vector Autoregressions

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Author Info

  • Gunnar Bårdsen

    ()
    (Department of Economics, Norwegian University of Science and Technology)

  • Helmut Lütkepohl

Abstract

Sometimes forecasts of the original variable are of interest al- 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 naive forecast of the original variable by simply applying the exponential transformation is not optimal theoretically. A simple expression for the optimal forecast un- der normality assumptions is derived. Despite its theoretical advantages the optimal forecast is shown to be inferior to the naive forecast if speci¯cation 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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File URL: http://www.svt.ntnu.no/iso/WP/2009/7_logVAR1.pdf
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Bibliographic Info

Paper provided by Department of Economics, Norwegian University of Science and Technology in its series Working Paper Series with number 10409.

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Length: 17 pages
Date of creation: 16 Jun 2009
Date of revision:
Handle: RePEc:nst:samfok:10409

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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. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  3. Helmut Luetkepohl & Fang Xu, 2009. "The Role of the Log Transformation in Forecasting Economic Variables," CESifo Working Paper Series 2591, CESifo Group Munich.
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Cited by:
  1. Lütkepohl, Helmut & Proietti, Tommaso, 2011. "Does the Box-Cox transformation help in forecasting macroeconomic time series?," Working Papers 1 OMEWP, University of Sydney Business School, Discipline of Business Analytics.
  2. Lorenzo Pascual & Esther Ruiz & Diego Fresoli, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," Statistics and Econometrics Working Papers ws113426, Universidad Carlos III, Departamento de Estadística y Econometría.

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