# Efficient numerical methods to estimate ARMA models?

I mean exact likelihood based estimation instead of these LS methods.

There are more general nonlinear optimization methods, but in terms of performance, are there any specific methods for this type of problems?

• One reasonably fast way to evaluate the likelihood is via the Kalman Filter. I believe at least some ML routines for ARMA models make use of this approach. – Glen_b -Reinstate Monica Apr 23 '13 at 3:45
• @Glen_b: Thanks, but since it is rather straight forward to compute the Hessian for ARMA with normal errors, I think the computation of likelihood is trivial in such cases... – user55647 Apr 23 '13 at 7:48
• It's straightforward in a variety of ways... but you asked about performance, not "triviality". Any optimization will involve function evaluations, so reasonably efficient methods become relevant, even if it's not hard to do it in a bunch of ways. – Glen_b -Reinstate Monica Apr 23 '13 at 8:29
• @Glen_b: I mean since solving the problem involves the computation of Hessian (typical), which is N^2 in size, so the evaluation of functions (N) is not likely to be the bottleneck of the performance when Hessian is computed analytically. – user55647 Apr 23 '13 at 8:44