We establish that ’s parameters are universally unidentified and a subset of their parameterization is over identified. As a solution to the problem with the identifiability, we propose a new representation of double-regime three-factor GDTSMs whose parameters are just-identified when the number of the pricing-with-error yields equals 2. This new parametrization has another advantage over  in that we can back out parameters and parameters separately and make the estimation of structural parameters easier. Finally, we show that regime-switching three-factor arbitrage-free dynamic Nelson-Siegel model is a restricted special case of our model.
Wang, G. (2014). Identification and Estimation of Gaussian Affine Term Structure Models with Regime Switching. Journal of Mathematical Finance, 04(03), 148–159. https://doi.org/10.4236/jmf.2014.43014