Riccardo Rebonato (R) has a fascinating new paper, which builds on important earlier work of Cieslak and Povala (2010) (CP).

The cool thing about CP is the way it advances and blends certain aspects of both the spanning literature ("all information of relevance for yield prediction is embedded in the current term structure," e.g. via forward-rate tent functions as in Cochrane-Piazessi (2004)),

*and*the non-spanning literature ("*not*all information of relevance for yield prediction is embedded in the current term structure," e.g. because certain macro variables seem to help predict risk premia, as in Ludvidson and Ng (2009)).
In turn, the cool thing about R is its insightful high-frequency / low-frequency interpretation of CP, with the macro predictors of primary relevance at low frequencies.

Adapted from the R abstract:

This paper presents a simple reformulation of the restricted CP return-predicting factor which retains by construction exactly the same (impressive) explanatory power as the original one, but affords an alternative and attractive interpretation. What determines future returns, the new factor shows, is ... the distance of the yield-curve level and the slope not from fixed reference levels, but fromconditionalones determined by ... long-term inflation.

I'm reminded of key early work by Kozicki and Tinsley (2001) on market perceptions of central bank credibility providing low-frequency anchoring for long yields.

More generally, high-frequency / low-frequency decompositions have a long and distinguished history in time-series econometrics, from cycle / trend real-output decompositions in macro-econometrics (e.g., Cochrane (1988)) to short-run / long-run volatility decompositions in financial econometrics (e.g., the "component GARCH" model of Engle and Lee (1999)).

More generally, high-frequency / low-frequency decompositions have a long and distinguished history in time-series econometrics, from cycle / trend real-output decompositions in macro-econometrics (e.g., Cochrane (1988)) to short-run / long-run volatility decompositions in financial econometrics (e.g., the "component GARCH" model of Engle and Lee (1999)).

A final thought: Bauer and Hamilton (2015) have recently questioned the entire non-spanning literature. Perhaps I'll cover that in a subsequent post, and its relation to CP and R (e.g., why worry about blending the spanning and non-spanning approaches if the non-spanning approach is suspect?).