Forecasting Levels of log Variables in Vector Autoregressions
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.
|Date of creation:||16 Jun 2009|
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- Helmut Lütkepohl & Fang Xu, 2012.
"The role of the log transformation in forecasting economic variables,"
Springer, vol. 42(3), pages 619-638, June.
- Helmut Luetkepohl & Fang Xu, 2009. "The Role of the Log Transformation in Forecasting Economic Variables," CESifo Working Paper Series 2591, CESifo Group Munich.
- 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.
- 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.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
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