Classical Principal Component Analysis

We go through the following steps to produce a vanilla principal component analysis.

1. Load raw spot yield data from the Bank of England website into a python dataframe
2. Truncate the data to create a rectangular matrix
3. Clean the raw data by:
   a. filling in blank values
   b. adjusting problem values
4. Transform truncated dataset into a calibration dataset by performing the following transformations:
   a. taking logarithmns
   b. differencing
   c. de-meaning
5. Calculate a co-variance matrix
6. Eigenvector and eigenvalue decomposition
7. Dimensionality Reduction
8. Projecting Co-ordinates

Steps

• standardise the data (mean zero and standard deviation 1)
• compute covariance matrix
• compute eigenvectors and eigenvalues
• sort components by explained variance
• choose number of components
• project the data using lower dimensional representation

to do

• cross check standardisation point