I know to use linear regression for an AR model and the Yule Walker equations for MA(1) model, but for an ARMA(1,1) or ARMA(2,1), do I use linear regression to obtain the autoregressive coefficients and ignore the moving average part and then use Yule Walker equations to get the moving average coefficients and ignore the autoregressive part(s)? Or is there a method that takes into account the whole model to obtain the parameters?

[NEAS: In practice, we use non-linear regression. We could use more sophisticated Yule-Walker equations, but no one does this now. The final exam will test the Yule-Walker equations only for MA(1).]