r"""
Litterman-Scheinkman: level, slope, curvature
=============================================

Litterman and Scheinkman (1991) ran a principal component analysis of
Treasury returns and found that three factors explain almost all of the
variation. They named them level, steepness (slope) and curvature. The
script repeats the analysis on synthetic daily yield changes and shows the
three loadings and their shares of variance.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from financialkit.fixed_income import simulate_yield_changes, yield_curve_pca
from financialkit.fixed_income.visualizers import plot_pca_loadings

tenors = np.array([0.25, 0.5, 1, 2, 3, 5, 7, 10, 20, 30])
changes = simulate_yield_changes(tenors, n_obs=2500, rng=1991)
pca = yield_curve_pca(changes, tenors)

# %%
# Loadings of the first three components
# --------------------------------------

plot_pca_loadings(pca)

# %%
# Share of variance explained
# ---------------------------

fig, ax = plt.subplots()
ax.bar(np.arange(1, tenors.size + 1), 100 * pca.explained_variance_ratio)
ax.plot(np.arange(1, tenors.size + 1), 100 * np.cumsum(pca.explained_variance_ratio), "ko-", label="cumulative")
ax.set_xlabel("component")
ax.set_ylabel("variance explained (%)")
ax.legend()
print("first three components explain", f"{100 * pca.explained_variance_ratio[:3].sum():.1f}%")
plt.show()