Looking at the time series of daily treasury yield curve rates, we can see that the several series are trending in a similar way, although their exact numbers are different. So it comes a question whether there are only a few forces that drive the trend. A factor analysis on time series would be an answer of it.
First, I de-trended the 11 series, and it looks like this way. The 1-, 3-, 6-, 12-month rates look alike, so do 2-, 3-, 5-, 7-year as a group, and 10-, 20-, 30-year as another.
Differenced U.S. Daily Treasury Yield Curve Rates from Jul 2012 to Jul 2014. The first column contains the differenced yield curve rates of 1-, 3-, 6-, and 12-month; the second column contains the differenced 2-, 3-, 5-, and 7-year rates; and the third column has the differenced 10-, 20-, 30-year rates.
While the 3-factor exploratory model essentially explains the similarity and difference between the series. Although the 4-factor model has better overall model fits, such as RMSEA, AIC, etc., it has one factor with all series loading low. So, I prefer the 3-factor model, and then it goes to the plots of the factor scores of the de-trended series, as well as back to the original factor scores.
Differenced Factor Scores of the 3-Factor Model.
Factor Scores of the 3-Factor Model.
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