yc_pca: Principal Component Analysis of Yield Curves

In yieldcurves: Yield Curve Fitting, Analysis, and Decomposition

Principal Component Analysis of Yield Curves

Description

Perform PCA on a time series of yield curves to extract the dominant factors (level, slope, curvature) following Litterman and Scheinkman (1991).

Usage

yc_pca(curves_matrix, n_components = 3, scale = FALSE)

Arguments

curves_matrix	Numeric matrix where each row is a yield curve observation (e.g., daily curves) and each column is a tenor. Column names should be maturity labels.
n_components	Integer. Number of principal components to retain. Default is 3 (level, slope, curvature).
scale	Logical. Whether to scale variables before PCA. Default is FALSE (use covariance matrix, standard in yield curve PCA).

Value

A yc_pca object (S3 class) with components:

loadings

Matrix of factor loadings (tenors x components).

scores

Matrix of factor scores (observations x components).

variance_explained

Numeric vector of proportion of variance explained by each component.

cumulative_variance

Numeric vector of cumulative variance explained.

sdev

Standard deviations of each component.

n_components

Number of components retained.

tenors

Column names from the input matrix.

References

Litterman, R. and Scheinkman, J. (1991). Common Factors Affecting Bond Returns. The Journal of Fixed Income, 1(1), 54–61. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3905/jfi.1991.692347")}

Examples

# Simulate 100 days of yield curves at 5 tenors
set.seed(42)
n_days <- 100
tenors <- c(1, 2, 5, 10, 30)
base_rates <- c(0.045, 0.043, 0.042, 0.040, 0.043)
curves <- matrix(NA, n_days, length(tenors))
colnames(curves) <- paste0(tenors, "Y")
level <- cumsum(rnorm(n_days, 0, 0.001))
slope <- cumsum(rnorm(n_days, 0, 0.0005))
for (i in seq_len(n_days)) {
  curves[i, ] <- base_rates + level[i] + slope[i] * (tenors - mean(tenors)) / 30
}
pca_result <- yc_pca(curves)
pca_result

yieldcurves documentation built on March 26, 2026, 5:06 p.m.