Discrete-time exponential-affine term structure models for calculating bond yields

I have derived a discrete-time exponential-affine term structure model on Laplace transform for calculating bond yields, and want to estimate it on appropriate yields, and possibly simulate it too for testing. The model structure is based on the model from the well-known article "Discrete-time Dynamic Term Structure Models with Generalized Market Prices of Risk" by Dai, Le and Singleton (DLS).

My model differs from their model by the expression of the state vector: X = (Z, Y)'. Under the risk-neutral probability measure (Q), their Z follows a AR(1) and Y a gamma/poisson diffusion.

Under Q, my Z follows a double autoregressive model DAR(1) ("Estimation and testing stationarity for double-autoregressive models" by Ling 2004), that is:

"Z_{t+1} = rho*Z_t + sqrt[w+a*Z_t^2]*e_{t+1}".

My Y follows another less well-known model (but natural extention of DAR):

"Y_{t+1} = rho'*X_t + sigma_t*e_{t+1} = \rho^Y*Z_t + rho_Y*Y_t + sigma_t*e_{t+1}",

where "sigma_t^2 = w^Y + a^Y*Z_t^2 + b^Y* Y_t^2".

Finally, I impose market price of risk to follow an affine function "Lambda = lambda0 + lambda1'*X_t", and the short interest rate "r_t = delta0 + delta1'*X_t".

When the state vector X is inserted in to the exponential affine Laplace transform the loadings for the term structure follow easily. They have a recursive structure like DLS, and it is worth noting that my loadings include Z in Z's loadings and Z and Y in Y's and X's loadings.

My task is to see if this change improves the models determination of yields, so I want to estimate the entire model, including recursive loadings. However, I thing I should start of with testing if it is at all feasible. Is there someone who has a code I can look at or can give me some advice on how to construct a code?

PS I have no experience with using Matlab.