classyguyyy / uk-yield-curve

PCA analysis on UK spot rates to model attributes of the yield curve

PCA Decomposition on the UK yield curve

Principal Components aims to reduce the dimensionality of a dataset; by finding the least amount of variables that explain the largest proportion of the data. It does this by transforming the data from a correlation matrix (more commonly used on financial data than a covariance matrix), onto a subspace with less dimensions, where all explanatory variables are orthogonal (perpendicular) to each other, i.e there is no multicollinearity. These are statistical properties and do not necesarrily have an economic interpretation.

For this analysis I will use the 10-year-yield for the US and UK to see if we can fiind an estimate for the long-term interest rate/term premium. It is commonly know that:

PC1: constant ~ long term interest rate ~ R*

PC2: slope ~ term premia

PC3: curvature

To read about this in more detail, read the PCA section of "Market Risk Analysis II, Practical Financial Econometrics- Carol Alexander".

There is also a good paper here which uses PCA and macroeconomic variables: https://pdfs.semanticscholar.org/8736/5855217edbc53e5e29c5c5872db7efb907cc.pdf

In this code I perform PCA manually, but there is a module in scikit-learn which speeds up the process:

https://github.com/scikit-learn/scikit-learn/blob/b194674c4/sklearn/decomposition/_pca.py#L104

A bit more detail on how to do PCA in Python: http://sebastianraschka.com/Articles/2015_pca_in_3_steps.html