CIR model fits Treasury yields better than two alternatives
Dante Amengual and Lluc Puig-Codina find that the Cox-Ingersoll-Ross (CIR) model outperforms Vasicek and 3/2 alternatives for Treasury yields. The Bank of Spain published their Bayesian analysis on October 26, 2026.
Exact inference without the barrier
The authors derive a full Gibbs sampler using the CIR model's exact transition density for equally spaced observations, avoiding numerical discretization.
They do not impose the Feller condition, which prevents the process from reaching zero.
Their framework supports smoothing and data missing at random; one tailored Metropolis-Hastings step extends estimation to irregular and random intervals under restrictions on observation timing.
For stationary processes observed at fixed intervals, they establish local asymptotic normality, consistent and asymptotically normal conditional maximum likelihood estimation and a Bernstein-von Mises theorem.
A hybrid sampler improves mixing by more than an order of magnitude.
Twenty years of weekly yields
The application uses 1,044 Wednesday observations of three-year U.S. Treasury yields from March 29, 2006 to March 25, 2026.
Log marginal likelihoods are -3915.436 for CIR, -4038.401 for Vasicek and -5591.406 for the 3/2 model, favoring CIR under the specified priors.
With a non-informative prior, CIR persistence averages 0.996, with a 95 percent credible interval of 0.991–1.001. The authors find that diffusion variance is tightly identified, while drift and the Feller index remain less precisely estimated.
Priors limit the verdict
The authors caution that persistence inference depends on prior choice.
Stationarity probabilities are 95.20 percent under the non-informative prior, 99.78 percent under the weakly informative prior and 24.03 percent under spike-and-slab.
Corresponding probabilities of satisfying the Feller condition are 86.70, 99.97 and 98.52 percent.