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  • $\begingroup$ At stats.stackexchange.com/a/35524/919 I answered a generalization of this question to spatial models. In summary, you can handle many time relationships with a "regular linear model," but often that is neither a parsimonious nor realistic way to do it. $\endgroup$ Commented Mar 2, 2021 at 20:47
  • $\begingroup$ You're absolutely right that regression is an extremely flexible way to estimate a probability model that would express several very complex types of autocorrelation. However, it's not a complete framework, and there are exploratory analyses specific to time series to try to suss out the proper way of estimating dependency structures, like variograms or spectral analyses. $\endgroup$ Commented Mar 2, 2021 at 22:27