## The Annals of Applied Statistics

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

### Functional dynamic factor models with application to yield curve forecasting

Spencer Hays, Haipeng Shen, and Jianhua Z. Huang

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 31 August 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1346418566

**Digital Object Identifier**

doi:10.1214/12-AOAS551

**Mathematical Reviews number (MathSciNet)**

MR3012513

**Zentralblatt MATH identifier**

06096514

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.aoas/1346418566

#### 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.Digital Object Identifier: doi:10.1214/12-AOAS551SUPP