Principal component analysis of yield curve movements

Principal component analysis of yield curve movements Article

Barber, JR, Copper, ML. (2012). Principal component analysis of yield curve movements . 36(3), 750-765. 10.1007/s12197-010-9142-y

An important issue in interest rate modeling is the number and nature of the random factors driving the evolution of the yield curve. This paper uses principal component analysis to examine (1) the inherent dimension of historical yield curve changes indicated by the significance of eigenvalues of the covariance matrix, (2) the practical dimension determined by a variance threshold, (3) the shape of the yield curve change associated with the first principal component, and (4) the persistence of this shape over time. We find that although the first two components explain 93% of the sample variation within a 90% confidence interval, the remaining components make statistically significant contribution to the covariance matrix. Consequently, we can establish a practical limit on the dimension only if we are willing to designate a threshold error variance. Further, our results on the persistence of the shape of the yield curve shift associated with the first component depend upon this threshold. If all components are included, the hypothesis that the shape persists between two sample time periods is rejected. On the other hand, if all but the first six components are eliminated, the hypothesis is not rejected. © 2010 Springer Science+Business Media, LLC.