PCA Analysis of US Treasury Yield Curve

This notebook performs Principal Component Analysis (PCA) on historical US Treasury yields to identify the main patterns of movement in the yield curve. It decomposes the yield curve into interpretable components such as level, slope, and curvature.

Overview

The US Treasury yield curve shows strong correlations between maturities, making it well-suited for PCA. This analysis extracts the first three principal components and interprets their economic meaning.

Analysis Steps

1. Data Processing

   • Load historical US Treasury yields for multiple maturities.
   • Align and clean data for PCA input.

2. Principal Component Analysis

   • Apply PCA to the time series of yields.
   • Calculate explained variance for each component.

3. Visualization

   • Explained Variance Plot: Shows how much variance each component explains.
   • Loadings Plot: Interprets each component in terms of yield curve shape.
     • PC1 – Level: Overall shift in interest rates.
     • PC2 – Slope: Steepening or flattening of the curve.
     • PC3 – Curvature: Mid-maturity hump or dip.
   • PC Scores Over Time: Tracks how each component's influence changes over time.

Key Insights

• PC1 generally accounts for the majority of variance and represents parallel shifts in the yield curve.
• PC2 captures short- vs. long-term rate differences (slope).
• PC3 highlights curvature changes, important in monetary policy analysis.

Requirements

• Python 3.x
• pandas, numpy, matplotlib, seaborn, scikit-learn

Usage

Open the notebook:

jupyter notebook pca_exp.ipynb