The Annals of Applied Statistics

Functional dynamic factor models with application to yield curve forecasting

Spencer Hays, Haipeng Shen, and Jianhua Z. Huang

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Accurate forecasting of zero coupon bond yields for a continuum of maturities is paramount to bond portfolio management and derivative security pricing. Yet a universal model for yield curve forecasting has been elusive, and prior attempts often resulted in a trade-off between goodness of fit and consistency with economic theory. To address this, herein we propose a novel formulation which connects the dynamic factor model (DFM) framework with concepts from functional data analysis: a DFM with functional factor loading curves. This results in a model capable of forecasting functional time series. Further, in the yield curve context we show that the model retains economic interpretation. Model estimation is achieved through an expectation-maximization algorithm, where the time series parameters and factor loading curves are simultaneously estimated in a single step. Efficient computing is implemented and a data-driven smoothing parameter is nicely incorporated. We show that our model performs very well on forecasting actual yield data compared with existing approaches, especially in regard to profit-based assessment for an innovative trading exercise. We further illustrate the viability of our model to applications outside of yield forecasting.

Article information

Ann. Appl. Stat., Volume 6, Number 3 (2012), 870-894.

First available in Project Euclid: 31 August 2012

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Functional data analysis expectation maximization algorithm natural cubic splines cross-validation roughness penalty


Hays, Spencer; Shen, Haipeng; Huang, Jianhua Z. Functional dynamic factor models with application to yield curve forecasting. Ann. Appl. Stat. 6 (2012), no. 3, 870--894. doi:10.1214/12-AOAS551.

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Supplemental materials

  • Supplementary material: Simulation studies and technical proofs. The online supplement contains the following: (1) additional simulation studies to further illustrate the advantages of our method; (2) detailed proofs of Theorem 2.1 and Propositions 2.1–2.4.