affine arbitrage free class of nelson siegel yield curve

I'm studying statistics for finance at university.

Last week i read the working paper on "The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models".

I would like to reproduce in R this work but i'm not able to understand the state space form of equations.

How can i estimate term adjustment?

• Why not write out the state space form of equations so that people can quickly understand your problem? We do not expect people will go to all details of a paper which may not be handily available. – Gordon Oct 30 '15 at 15:24
• i'm sorry. the measurement equation is : – frank Nov 1 '15 at 12:14
• yt = A + BXt + εt. y is a vector Nx1 of observed yield, A is a Nx1 vector of adjustment term, B is matrix Nx3 of this form: 1 (1−e−λτ) ((1−e−λτ)−e−λτ) where lambda is a parameter to estimate and tao is the Maturity. X is the state variables. The state equations is: – frank Nov 1 '15 at 12:35
• Xt = (I − exp(−K * ∆t))*θ + exp(−K *∆t)*Xt−1 + ηt where I is diagonal matrix of 1, K is a non- diagonal matrix of parameters to estimate, θ is a vector Nx1 of parameters to estimate and ∆t is the time to maturity. i hope that you can understand, if you need more information write me. thank you so much @Gordon – frank Nov 1 '15 at 12:45
• Comments are meant to be temporary, can you edit the formulae into the question itself using $\LaTeX$? – Bob Jansen Nov 1 '15 at 18:42