We then provide a synopsis of the primitive models we average over, followed by a section describing the types of model averaging we consider.
Such a choice, however, contrasts with our goal of providing evidence on the benefits of model averaging relative to model-selection techniques.
(5) With this rich collection of individual forecasting models as building blocks, we consider a range of approaches to model averaging with an eye toward determining which types of model averaging are most useful and moreover, which types of primitive models are the most useful for averaging over.
While these methods are not statistically exciting, substantial evidence suggests that simple forms of model averaging can perform quite well (e.g., Smith and Wallis, 2009).
We then consider two distinct forms of weighted model averaging. In the first, we follow Stock and Watson (2004) (among others) and consider relative inverse mean square forecast error (MSE)-based weights to combine our models.
For the top 10 percent MSE models this is done by averaging over only the models with the lowest 10 percent of pseudo out-of-sample MSEs based on the data available as of the forecast origin.
In reporting our results it is useful to gain some perspective on the magnitude of the benefits of model averaging. Doing so requires choosing a baseline for comparison.
For each variable and each horizon, we consider six different forms of model averaging: average, median, (inverse) MSE-weighted, BIC-weighted, top 10 percent (inverse) MSE-weighted, and top 10 percent BIC-weighted.
In this section, we discuss our results on the benefits of using forecast averaging as a tool for improving forecast accuracy.
At the three shortest horizons there are few, if any, advantages to forecast averaging across all models in terms of RMSEs.
In contrast to the results for headline inflation, consistent improvements are noted at all horizons for model averaging across all models.
The first and second panels of Table 2 parallel those in Table 1 in terms of the benefits of model averaging. As for headline CPI, model averaging across all models provides little to no improvement relative to model selection when forecasting IP growth at the shortest horizons.