Given a time series, I'd like to estimate the parameters of an AR(1) model for it. As explained on wikipedia, there are different ways for doing that. What may be called a naive method is to compute the sample mean, variance, and autocovariance of the sample and then obtain the parameters of the AR(1) model using some simple equations. Alternatively, one can use more complicated things like maximum-likelihood estimation.
What is the benefit of one method versus the other?
Are there any provable differences? For example, suppose my data really comes from an AR(1) process, is the "naive" method provably less accurate than others such as maximum-likelihood?