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In this paper we survey a number of recent empirical findings regarding the usefulness of including diffusion indexes in dynamic Nelson-Siegel (DNS) type models used to predict the term structure of interest rates (see e.g., Diebold and Li (2007) and Diebold and Rudebusch (2013)). We also survey various empirical methods used in the construction of DNS models, and used to specify and estimate diffusion index augmented DNS models. In particular, we review (sparse) principal component analysis, factor augmented autoregression, and various dimension reduction, variable selection, machine learning, and shrinkage methods, such as the least absolute shrinkage operator (lasso), the elastic net, and independent component analysis, among others. Finally, we discuss the importance of using real-time data in contexts where datasets are subject to revision; and we compare and contrast the use of targeted versus un-targeted specification methods when including diffusion indexes in DNS type prediction models. Interestingly, as noted in Swanson and Xiong (2018a, 2018b), the usefulness of diffusion indexes is crucially dependent upon whether real-time data are used or not. Specifically, when real-time data are used to estimate the weights in di usion indexes, it is found that relatively few “data rich” models that use big data are preferred to simpler DNS models, post 2010. Instead, pure DNS models that rely only on historical interest rate data deliver mean square error “best” forecasts. However, when data are not real-time, diffusion indexes always have marginal predictive content for interest rates. Moreover, it is clear that in more volatile interest rate regimes, such as prior to 2010, machine learning and related methods have much to offer, regardless of the type of dataset used in their construction.

A survey of dynamic Nelson-Siegel models, diffusion indexes, and big data methods for predicting interest rates