I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some optimization routine.

Question:Why rewrite the model into its state space representation and maximize the corresponding likelihood — instead of maximizing the “naive” or “direct” likelihood?(I could imagine that a different parameterization can make the optimization easier — is that the case here?)

Related questions:

- “Comparison of estimation techniques for ARIMA model”
- “What state-space representation of VARMA is commonly used for fitting”
- “What is the requirement for Kalman filters”
I am also aware of some general advantages and disadvantages of the state space representation as mentioned in “What are disadvantages of state-space models and Kalman Filter for time-series modelling?”.

**Answer**

**Attribution***Source : Link , Question Author : Richard Hardy , Answer Author : Community*