Burn-In and Validation for Simulated AR(1) State Space Models
Summary
The discussion asks how to simulate observations from a state space model whose latent state follows an AR(1) process. It focuses on whether to discard initial observations as burn-in so the simulated process approaches its stationary distribution, and whether matching simulated estimates to theoretical moments is enough to validate an implementation. The response says that one lag may be sufficient for AR(1) burn-in, while suggesting a longer warm-up as a more cautious choice.
For validation, the answer cautions that exact agreement with theoretical values should not be expected from finite simulated samples. It suggests using AIC or BIC on simulated data to help select among candidate models and notes that log-likelihood values can be obtained through Kalman filtering or estimation functions in MATLAB. The reply is brief and does not derive a burn-in length, quantify sampling error, or provide a method for constructing parameter confidence bounds. Its recommendations therefore offer starting points rather than a full simulation-validation procedure.
Key ideas
- An AR(1) state process may need an initial burn-in period before its observations are used.
- The response suggests one lag as a possible burn-in and a longer warm-up for added comfort.
- Finite simulated samples should not be expected to match theoretical moments exactly.
- AIC and BIC on simulated series may help compare candidate models.
- The discussion does not provide formulas for burn-in selection or parameter error bounds.
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Full text
# Simulating state space model with AR(1) dynamics # Simulating state space model with AR(1) dynamics I asked a question similar to this previously: https://dsp.stackexchange.com/questions/16341/simulating-a-state-space-model 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. http://www.mathworks.co.uk/help/econ/simulate-stationary-arma-processes.html 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? Baz ## Answer by user12348 (score 1) https://quant.stackexchange.com/a/11530 Q1- for AR(1) only one 1 lag, ie burn in, should be sufficient. However, you could do 50 to feel comfortable. Q2- Matching the theoretical one is not a possibility Q3. (update) AIC/BIC tests on the simulated series can help select the best one. You can get the logL values from KF or estimate functions in Matlab.
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