Using Yield Curve Changes for Principal Component Analysis

Summary

The document asks whether principal component analysis (PCA) is appropriate for interest-rate term structures that appear non-stationary, and whether a Kalman filter would be preferable. Its answer recommends applying PCA to changes in yield-curve points, which may be more stationary, rather than to their levels. The covariance matrix of those changes can reveal common patterns in curve movements.

The example interpretation is that a leading component may represent a parallel shift in rates. The note offers this as a practical interpretation, not a detailed empirical study: it provides no data, tests, or comparison with Kalman filtering. The suitability of the approach therefore depends on the properties of the observed changes and the research question; the document does not establish that changes are always stationary or that PCA is universally better than filtering.

Key ideas

• PCA on yield-curve levels may be problematic when the series are non-stationary.
• Applying PCA to changes in curve points may be more appropriate if those changes are stationary.
• A principal component can capture a parallel shift in the yield curve.
• The note does not provide evidence comparing PCA with a Kalman filter.

Tags

# PCA on term structure of interest rates


# PCA on term structure of interest rates












Interest rate time series seems to be non-stationary whenever test is performed

But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA is performed on that covariance or correlation matrix.

Is it appropriate to derive Covariance or correlation matrix from non stationary series and use it for PCA?

Applying Kalman filter on term structure of interest rates is any better than PCA?

## Answer by Richi Wa (score 2, accepted)

https://quant.stackexchange.com/a/15546

If you look at changes of the points on the yield curve, then you probably find something stationary - right? Applying PCA on the covariance of these changes makes sense.

E.g. you will find out that on PC describes a parallel shift (a change in the yield curve). Look at this question too: What do eigenvalues/eigenvectors of the yield/forward rates covariance matrices mean?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.