Imports the interest rate series [Daily yield curves of monthly maturities up to a year].

Creates the stationary series of the differences.

The mean of the series is relatively small, which implies that there is no substantial drift in the series.

The correlation is quite high for similar maturies, and it is decreasing as the horizon differences increase. This is shown in the following 7×7 submatrix of the 12×12 original correlation matrix. Only a submatrix is presented for space reasons.

The eigenvalues and eigenvectors are going to be useful for the principal component analysis. The eigenvectors represent the factor loadings, while the eigenvalues represent the significance of the factors. Note that they are reported in descending order.

The relative weights of the eigenvalues give us the explanatory power of the various factors. The first factor explains 82.6% of the variability, the second 9.5%, the third 2.6%, and so on. The first three factors combined will explain 94.7% of the variability of the series.

The matrix of the components is created. By construction, and unlike the original series, the components are mutually uncorrelated.

Every element of the original series can be reconstructed using the components and the matrix of the loadings.

As reported in the interest rate literature, the three factors represent different aspects of interest rate movements: The first factor is responsible for level shifts, the second one for slope changes and the third one for convexity adjustments.

One can use the first three loadings to generate the components that will replicate the original series in the best way [in a least squares sense]. The loading matrix is shown transposed for space reasons.

The covariance matrix of the components is again the matrix of the eigenvalues.

Of course, the components are not the same as before.

The constructed series will resemble closely the original ones. The prediction errors for the one, six and twelve month interest rate are presented. Note that most differences are substantially below the 0.1% level.