Bias corrections for exponentially transformed forecasts: Are they worth the effort?

In many economic applications, it is convenient to model and forecast a variable of interest in logs rather than in levels. However, the reverse transformation from log forecasts to levels introduces a bias. This paper compares different bias correction methods for such transformations of log series which follow a linear process with various types of error distributions. Based on Monte Carlo simulations and an empirical study of realized volatilities, we find no choice of correction method that is uniformly best. We recommend the use of the variance-based correction, either by itself or as part of a hybrid procedure where one first decides (using a pretest) whether the log series is highly persistent or not, and then proceeds either without bias correction (high persistence) or with bias correction (low persistence).