Mixing Mixed Frequency and Diffusion Indices in Good Times and in Bad

In the field of economics, recent advances in the areas of machine learning, shrinkage, and variable selection have been spectacularly successful. In one key area of study, advances in both modelling and estimation have enabled empirical practitioners to show the usefulness of latent factors designed to efficiently extract common information from interesting new datasets. At the center of this big data success are di¤usion and mixed frequency indices, which have proven useful time and time again in forecasting contexts. This paper lends further support to recent claims of the usefulness of these sorts of indices, albeit with a twist. We show that the usefulness of said indices is pronounced during low GDP growth periods, while simple autoregressive models are adequate during high growth periods. This finding stems from the introduction of very simple hybrid models that employ dynamic recursive (rolling) thresholding in order to switch between benchmark linear models and more complex index driven models, depending on GDP growth conditions. In the context of predicting both quarterly real GDP growth and CPI inflation, these hybrid models are found to be superior, for all forecast horizons. When comparing the hybrid models against a host of alternatives, mean square forecast error gains reach as high as 35%, during the Great Recession, and remain significant throughout our entire prediction period. Additionally, the very best short-term GDP forecasting models contain variants of the Aruoba, Diebold and Scotti (2009) business conditions index, although these models are most useful when di¤usion indices are also incorporated. Thus, mixing mixed frequency and di¤usion indices matters. Finally, across all experiments, we find strong new evidence of the usefulness of survey predictions, including those from the Survey and Professional Forecasters, and those from the Livingston Survey