Hi everyone,
I posted a similar question on the R-help list a few days ago and it
was suggested to me to try here instead. I apologize for the
cross-posting.
I'm trying to model a term structure of yield spreads where the state
variables are independent square-root processes.
The state space model I want to estimate using a Kalman filter takes
the following form -
measurement eq:
z_t = a + b*y_t + eps_t
transition eq
y_t+h = (I -exp(-hL))theta + exp(-hL)y_t+ eta_{t+h}.
The problem is that the distribution of the error terms of the
transition equation depend on the previous value of the state
variable.
To be exact: y_t|y_{t-1} ~N(mu, Q_t) where Q is a diagonal matrix with
elements equal to
Q_{i,t} = sigma_i*(1-exp(-kappa_i*h)/kappa_i*(theta_i/2*(1-exp(kappa_i*h)+exp(-kappa_i*h)y_{t-1,i}
I found an old thread about the same problem
https://stat.ethz.ch/pipermail/r-sig-finance/2007q2/001362.html
I've adapted Prof. Silva's code by to my setting, but the optimization
process breaks down.
Any ideas or examples on how to solve this problem are much appreciated.
Thank you in advance.
Kristian