Calculate the Covariance Matrix

Notation

The covariance matrix $\mathbf{A}$ (see the notation reference in Notation) is computed from the demeaned log-differenced yields $\widetilde{\mathbf{Y}}_c \in \mathbb{R}^{(T-12)\times N}$ produced in Step 5:

$$\mathbf{A} = \frac{1}{T-13}\widetilde{\mathbf{Y}}_c^\top \widetilde{\mathbf{Y}}_c$$

$\mathbf{A} \in \mathbb{R}^{N \times N}$ — one row and one column per maturity, so entry $a_{i,j}$ is the sample covariance between maturity $i$ and maturity $j$.

step 1 - calculate the covariance matrix

import subprocess  
%run ./dataframes/step6_covariance.py  
%run ./dataframes/truncate_with_ellipsis.py  
df = covariance_matrix()  
subprocess.run(['wl-copy'], input=truncate_with_ellipsis(df, 3).to_html(index=True).encode())  

Python

filename: step6_covariance.py

from dataframes.step5_demeaning import *

def covariance_matrix():
    df = demeaning()
    value_cols = df.columns[1:]
    Y_c = df[value_cols]
    n = Y_c.shape[0]
    A = (Y_c.T @ Y_c) / (n - 1)
    return A