Statistical Inference
Inference for Parameters
You can get posterior samples of the term structure model parameters using reducedform.
reduced_params = reducedform(saved_params, yields, macros, tau_n; data_scale=1200)yields is a T by N matrix, and T is the length of the sample period. N is the number of bond maturities in data. tau_n is a N-Vector that contains maturities in data. For example, if there are two maturities, 3 and 24 months, in the monthly term structure model, tau_n=[3; 24]. macros is a T by dP-dQ matrix in which each column is an individual macroeconomic variable.
We estimate the $\mathbb{P}$-VAR by transforming it into a recursive VAR form. Therefore, Parameter, the output of posterior_sampler, contains parameters in the recursive VAR. In contrast, ReducedForm, the output of reducedform, contains parameters in the original reduced-form $\mathbb{P}$-VAR.
Each entry in reduced_params::Vector{ReducedForm} is a joint posterior sample of the parameters.
Yield Curve Interpolation
We first have to transform the parameter space from the principal component space to the latent factor space. It is done by latentspace. And then, use fitted_YieldCurve to get fitted yields. Specifically,
saved_latent_params = latentspace(saved_params, yields, tau_n; data_scale=1200)
fitted_yields = fitted_YieldCurve(τ0, saved_latent_params::Vector{LatentSpace}; data_scale=1200)τ0 is a Vector containing the maturities for which we want to calculate fitted yields through interpolation. fitted_yields::Vector{YieldCurve} contains the results of the interpolation.
Term Premiums
term_premium calculates the term premium of τ-maturity bond. τ should be a scalar.
saved_TP = term_premium(τ, tau_n, saved_params, yields, macros; data_scale=1200)saved_TP::Vector{TermPremium} contains the results of the term premium calculations.