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When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?

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    $\begingroup$ From my experience the higher PC:s have more complex shapes so the interpretation is more complicated as well. Also the above terms are not perfect, e.g. PC1 is not exactly a level factor and can show a weak slope pattern. $\endgroup$
    – fes
    Mar 3, 2022 at 14:34

1 Answer 1

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The first 3 PCs have clear geometric interpretations: PC 1 is “level” or “parallel shift”; PC 2 is “slope” or “tilt” or “flatness / steepness” or “twist”; and PC 3 is “curvature”, “bow”, or “butterfly”.

However the higher-numbered components have less intuitive geometric interpretations, such as “double-humps” at varying tenors. Some discussion of PCs beyond 3 can be found in: Richard K. Crump and Nikolay Gospodinov (Federal Reserve Bank of New York). Deconstructing the Yield Curve. Staff Report No. 884 (Revised January 2022).

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