No. 7/2009: FORECASTING LEVELS
OF LOG VARIABLES IN VECTOR AUTOREGRESSIONS REFORM. Gunnar Bårdsen and
Helmut Lütkepohl
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.
