I asked a question similar to this previously:
However I think I have a better handle on it now and want to re-ask it:
I simply want to simulate data from a state space model where the state variables follow an AR(1) process (see the code in the first link above).
Given the burn in issues (see link below) I assume it's better to determine empirically how many observations are required until the system reaches its theoretical unconditional variance then ensure that I simulate at least 2 times that amount before using the x(t) generated by the AR(1) process in my state space model.
Q1.) If I want to simulate data from my state space model is it necessary to ensure that the AR(1) process is in it's equilibrium state first?
Q2.) From the simulated data I will be able to estimate the observation and state error variances as well as the AR(1) parameters and the unconditional mean and variance of the process (averaged over many sample runs). Assuming these empirical values all match their corresponding theoretical ones, can I then be fully satisfied that the state space model which is based on the AR(1) process has been implemented correctly?
Q3.) How can I estimate what the likely error bounds should be on the parameters that I propose to estimate in Q2?