The effect of aggregation and the log transformation on forecasting.

Abstract

Many economic variables are used in logarithms for forecasting and estimation analysis, as this transformation is considered to create a more homogenous variance. The aim of this study is to investigate whether applying logs to the variables of interest improves forecasting precision. Forecasts based on logs are compared to forecasts based on the original series, both for univariate time series and aggregates. Furthermore, forecasts of the aggregates are compared to those obtained by aggregating the forecasts of the individual components based on levels and on logs. The results show that for univariate time series, using logs can be beneficial for forecasting as long as it stabilizes the variance. Otherwise, applying logs can provide inferior forecasts. When it comes to aggregated variables, using logs is often beneficial, especially for long forecast horizons. If logs are not applied, it is preferable to aggregate the forecasts of the components rather than forecasting the aggregate directly only for long forecast horizons.