Abstract
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.
Highlights
The term structure of interest rates plays a important role in asset management
This amounts to taking a “snapshot” of the data that are available at a particular point in time, and assuming that the historical elements of that data are never revised, even when carrying out real-time forecasting experiments in which dynamic Nelson-Siegel (DNS) hybrid DNS, and factor augmented regression models are re-estimated at each point in time, prior to the construction of each new forecast
We focus on the use of “un-targeted” prediction, in which case diffusion indexes are extracted from a large dataset, and the diffusion indexes that are utilized in forecasting models are those that are the most information rich, in the sense that they explain the largest share of the overall covariance matrix of all of the variables in the dataset
Summary
The term structure of interest rates plays a important role in asset management. One reason for this is that interest rates contain important information for pricing interest rate contingent assets. Historical inflation rates are regularly revised, and so if one specifies a hybrid DNS type model that includes diffusion indexes that are constructed using inflation (and other revised macroeconomic variables) one must account for the fact that inflation data are subject to revision These findings are based on analyses that utilize real-time datasets, as well as analyses that assume all data are fully revised In the latter case, this amounts to taking a “snapshot” of the data that are available at a particular point in time, and assuming that the historical elements of that data are never revised, even when carrying out real-time forecasting experiments in which DNS hybrid DNS, and factor augmented regression models are re-estimated at each point in time, prior to the construction of each new forecast.
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