Does modal (auto)regression produce credible forecasts of macroeconomic indicators?

Modal regression is a relatively new statistical technique that serves the purpose of modelling the modal value of a variable conditional on a set of explanatory variables. The aim of the study discussed in this paper is to assess the usefulness of modal regression in the analysis of economic time series and, more specifically, in short-term macroeconomic forecasting, on the example of industrial output indexes of 27 OECD countries. We focus on models of univariate time series and pose a question whether linear and nonlinear (threshold type) modal autoregression leads to more trustworthy macroeconomic forecasts than standard approaches based on modelling other measures of central tendency. The credibility of forecasts is understood as appropriately defined accuracy of point forecasts, and as narrow forecast intervals. Our empirical results demonstrate that linear modal autoregression can compete with other linearly-specified models both in terms of the aggregate forecast accuracy and the lengths of prediction intervals. It should be mentioned, however, that in the case of the study described in this paper, carried out on the data sample spanning the period from January 1994 to December 2019 and the period of forecasting allowing the determination of 100 forecasts in time horizon from one to four months according to the rolling schema, narrower prediction intervals in comparison with other estimation methods have turned out more likely for lower nominal confidence levels such as 80% and below, while differences in precision measurements, including credibility differences, have rarely proved statistically significant. Our analysis also shows that narrow-interval forecasts of economic growth rates might require specifying a GARCH equation, but on the other hand, at certain confidence levels and forecast horizons, models with GARCH equations might be outperformed in this respect by nonlinear (in mean or mode) autoregression. Another interesting fact is that modal autoregression minimises the robustified sMAPE indicators for one-step-ahead forecasts of the output indexes.