Estimating the Term Structure: Principal Component Analysis

This lecture focuses on Principal Component Analysis (PCA) as a dimension reduction technique in multivariate data analysis to find basis shapes of the yield curve. The Spectral Theorem is explained as the mathematical principle underlying PCA, followed by the decomposition of the covariance matrix. Properties of the principal components, explained variance, and their application in interest rate models are discussed. Sample principal components, empirical mean, covariance, and their decomposition are also covered. The lecture concludes with a discussion on the PCA of the yield curve, including yield curve loadings and the explained variance of principal components.