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The yield curve can be explained using a PCA, where the cumulative proportion explained for many practical purposes is high enough with three factors.

For one set of data, used at https://www.r-bloggers.com/principal-component-analysis-to-yield-curve-change/ they explained 58% with factor1 and 85% by adding factor2 and 93% by adding factor3. This is inline with other data sets I have seen, e.g. Tsay - Analysis of Financial Time Series.

The three factors are interpreted from the signs and size's of the coef as "shift, twist and curvature". Since curvature explains the least amount of variability, does that imply shifts happen more seldom in the real world than a shift does? I.e. does the ordering tell us something about the frequency with which they occur? Or is it just that when shifts do happen the change the look so much that it is the first principal component?

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Re: does the ordering tell us something about the frequency with which they occur?

No it doesn't. It's more about how much this component contributes to the final variance. Probably every bit of move of the yield curve contains some extent of curvature change. It's just a matter of how much of it can be explained by the variables.

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