Estimating Gaussian ATSMs

We introduce some notable approaches to estimate Gaussian ATSMGaussian ATSM using linear regressions. Consider a general Gaussian ATSM given as Then, by Affine Term Structure Models > ^72d83fAffine Term Structure Models > Corollary 7 (Ricatti equations for GASTM), the yields are given as an affine function of the factors: where and are functions of the parameters In practice, we assume that there exists a measurement error for yields so that the model can be written in State-Space ModelState-Space Model form as where is the covariance matrix of the measurement errors.

The full estimation of the model parameters will be performed based on Gaussian MLE or Bayesian estimation via the Metropolis-Hastings algorithm, using Kalman filter and smoother, tor Carter-Kohn's backward recursion. Due to the large number of parameters in the model, the likelihood function shows high irregularity.

The following three approaches take inspirations from Doz, Giannone, and Reichlin (2011) and assumes that the factors are observable functions of the data. Here, the factors are obtained principle components of the yields or linear combinations of the yields assuming that the measurement errors do not exists in certain maturities. In all of the three methods, the factors are taken to be affine transformations of the yields.

See Adrian, Crump and Moench (ACM)Adrian, Crump and Moench (ACM)