Therefore, people stick with relatively performant & interpretable methods such as ARIMA and friends.
Additionally, most TS problems are relatively data constrained (your company/product has only existed for so long) so methods that are sample efficient (which most "modern" ML methods are not) are much more useful.
Also, time series/forecasting is a ghetto ;)
The problem isn't the math, the problem is people are not rational.
But the fact is, ARIMA models work. So people keep using them. And you can see what they're doing, and understand why, and how to tune them.
It's also not considered a good general default choice for time series forecasting, but that's another story.
One of the things that confused me is that regression models can be predictive, just like time series forecasting — they just do so in a different way. I tried to make this clear in the article (or maybe I’m not understanding what you’re saying).
In a regression model, you’re predicting target variables from feature variables. In a time series, you’re predicting the same variable from its past behavior. This is a subtle but crucial difference.
(And then you can do time series with covariates, which combines the two.)
I should say that I enjoyed this post. And I think leaning into that confusion is my aim. In particular, my point of stochastic versus random is that they are more synonym than they are anything else. Just words that different groups came to use covering similar things.
Which is not to say that their aren't differences in the crowd that uses each term. I posit that most of the differences is in the aims of the crowd, and at the end of the day, you can get a lot of mileage by embracing the similarities. As opposed to the default of contrasting on the differences.
As a fun example, to me, if you view time not as just a number that always goes up, but as a number that cycles through the seasonal values, then it is easy to view as most any other feature. Similarly, the past is easy to envision as a feature of the present.
I do think the way you described a lot of time series analysis fits the fun read I had where Mandlebrot proposed a fractal view of time series predictions. Where you are looking for self similar behavior in the series data and reflecting/overlaying it on itself. But... as is probably guessable from the rest of my post, a lot of this is far outside of my comfort area. Love reading about it from a distance.
If you are using them to extrapolate (eg. Prediction) that should help you gauge how resilient you expect the model to be in prediction.
Obviously, for ARIMA the AR and MA parameters aren't very informative.
I use SARIMAX a decent amount, nonetheless.
The quality is significantly lower than a good article written by a competent human, but maybe on par with or slightly better than a trashy article written by a content farm.
The advantage of the chat interface is that you can ask it clarifying questions. The real benefit of generative AI would be something like Copilot that you can interrogate for clarification as you are working through an article written by another human.
That, and the other problem of AI being trained on AI until nobody knows anything anymore.
In terms of forecasting state of the art are weather models like graphcast or panguweather. I guess arima won't be much of help in those high dimensional cases.
If you consider the univariate case the trick to outperform arima I guess is to detect the context from the time window before to make better contextual predictions: this is much like a regression on a hidden variable.
Extrapolation (predicting an unknown future), and interpolation (estimating unknown present/past) are not really that different.
If you take however the example of the weather as an extreme example of time series forecasts, downsizing eddies or forecasting them in a navierstokes surrogate, this can require some different approaches.
According to this article, to make good predictive/regression model, we need a good artist and a good engineer!
I was wrong.
