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I have Treasury yield data across 11 maturities for past 1 year. I have used a code in MATLAB for PCA on change in yield curve. Now, I have covariance matrix of daily/monthly yield curve changes, principal components and the fractions (individual and cumulative) explained by the principal components.

So with this data, how do I conclude if a parallel shift model is a good way to describe fluctuations of the yield curve over this time period ?

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Based on factor loadings you should be able to tell if the first component is a parallel shift (if you did everything correctly it's highly like that it is). The variance explained by the factor then a measure of how good that model is. Note that a parallel shift normally actually isn't fully parallel, but instead has different weights on the front and back of the curve (but with all the same sign)

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your PCA's are effectively the eigen-values and the eigen-vectors of the covariance matrix.

The eigen-values (corresponding to each eigen-vector) show the proportion of (orthogonal moves) that is explanable by each eigen-vector. Usually, the first eigen-vector (i.e. 1st PCA) will have a eigen-value (relative to the sum of all eigen-values) that shows it explains >90% of the moves.

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