## Hoisted from Five Years Ago: Department of "Huh?": Estimating Long-Run Properties of Time Series

**: Department of "Huh!?": This Is All Cosma Shalizi's Fault Department...: 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?

Low-order ARMA models are bad guides to the (very limited) information present about the long-run behavior of time series.

Low-order AR models are even worse...