Is autoregressive models linked to delayed time series embeddings and taken’s theorem in some way?
Btw love the day 2 tutorial, big fan of dynamic mode decomposition, only hope that we can go more in-depth
The method of embedding space reconstruction using Takens’ theorem is a little bit more general: it allows you to visualize possible nonlinear relations between the delayed components, which you wouldn’t normally see in simple (linear) autoregressive modelling.
So autoregressive models only include models with linear relationship to it’s past components?
I am just thinking since time lagged reconstruction guarantees diffeomorphic correspondence between original and embedded manifold, is it in a way saying that a dynamical system with many variables can be transformed to a autoregressive model with one variable with generally similar dynamics?
There are nonlinear autoregressive models out there, but usually you need to have an idea of the function that makes the connection to the past components or guess using clever strategies. These are certainly not the first thing you think of when saying just autoregressive model
Second question is tricky, I have to think about it a little further… intuitively, I would agree with your suggestion, but have to check.