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Forecasting levels of log variables in vector autoregressions

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  • Bårdsen, Gunnar
  • Lütkepohl, Helmut

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/ijforecast

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Keywords: Vector autoregressive model Cointegration Forecast root mean square error;

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  1. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, vol. 42(3), pages 619-638, June.
  2. 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.
  3. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198774501, October.
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Cited by:
  1. Tommaso, Proietti & Helmut, Luetkepohl, 2011. "Does the Box-Cox transformation help in forecasting macroeconomic time series?," MPRA Paper 32294, University Library of Munich, Germany.
  2. Lorenzo Pascual & Esther Ruiz & Diego Fresoli, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws113426, Universidad Carlos III, Departamento de Estadística y Econometría.

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