I am trying to estimate aHeston model using an Unscented Kalman filter. In particular, I am using the following Euler-Murayama discretisation:
Where z1[t] and Z[t] are standard normal random variables. Please note that I have already decomposed the correlation in the two Brownian motions in these two state equations. So given this, I have two state variables that are non-stochastic in period
V[t]) and two state variables that are fully stochastic in period
z2[t]). As such, my question is regarding choosing and picking the sigma points. The intuition I have is that since the only stochastic random variable at time
z2[t], this implies that my sigma points will only depend on these two variables which are iid across time, right? Thus, the covariance matrix of the sigma points will be constant across time. Is my intuition right? Thank you.