In this paper we give explicit expressions for the forecasts of levels of a vector time series when such forecasts are generated from (possibly cointegrated) vector autoregressions for the corresponding log-transformed time series. We also show that simply taking exponentials of forecasts for logged data leads to substantially biased forecasts. We illustrate this using a bivariate cointegrated vector series containing US GNP and investments.

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Keywords VAR time series, forecasting, log-transformation
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Journal International Journal of Forecasting
Ariño, M.A, & Franses, Ph.H.B.F. (2000). Forecasting the levels of vector autoregressive log-transformed time series. International Journal of Forecasting, 111–116. doi:10.1016/S0169-2070(99)00025-4