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Forecasting Levels of log Variables in Vector Autoregressions

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  • Gunnar Bardsen
  • Helmut Luetkepohl

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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Bibliographic Info

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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Keywords: Vector autoregressive model; cointegration; forecast root mean square error;

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  1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  2. 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.
  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. 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.
  2. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.

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