Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, but I also see the issue when doing my own PCA through Numpy. So as far as I know it's not an issue of the libraries.

After I get the vectors I solve the linear equations such that the first two principle components sum to 0. This is done by setting one of the weights = 1.0

Here's an example. I have data for 150 settlements and I calculate the PC's using data from day 0-100, then I recalculate 10 days later on data 10-110, etc.

When I do this I get a graph of the PC's

And here are the corresponding weights.

Relevant math: After performing the PCA I get the components matrix $~ \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)$ From here I take the first two vectors $[a, b, c]$ and $[d, e, f]$. Which I then turn into the equation $Ax = B$ that looks something like this $~ \left( \begin{array}{ccc} a & c \\ d & f \end{array} \right) \left(\begin{array}{ccc} x_1 \\ x_3 \end{array} \right) = \left(\begin{array}{ccc} b \\ e \end{array} \right)$

As you can see the $x_1$, $x_3$ weights start to blow up at some point which doesn't really make sense given the nature of the data.

Does anybody have any insight to my problem?

• When you say "a couple" do you actually mean 2? Your second and third components look to be extremely highly (negatively) correlated, suggesting you could have some sort of linear dependence.
– will
May 13, 2017 at 10:58