So when something comes across my RSS feed stating that it is "2500 words of statisticians quarreling with econometricians about arcane points of statistical theory", how am I supposed to resist getting sucked in?

And so not that many minutes later I find myself reading:

Chris Sims: Time series econometricians long ago got over the idea that frequency domain estimation, which makes only smoothness assumptions on spectral densities, is any more general than time-domain estimation with finite parametrization. In fact, the preferred way to estimate a spectral density is usually to fit an AR or ARMA model…

But surely if you are, to pick an example out of thin air, interested in estimating how much of a time series is made up of its permanent or near-permanent persistent components, you should estimate *that* directly--not use short-run autocorrelations to fit a low-order ARMA process and then infer the permanent and near-permanent persistent components from the low-order ARMA representation.

In what sense can "fit[ting] an AR or ARMA model" be the "preferred" way to conduct such an esimation?