Just wanted to ask a qualitative question in terms of the AR(1) having an infinite MA representation.
Firstly, here, in reverse order: I can understand why it is important to ensure that an MA process has an infinite AR representation (i.e. the MA/white noise process is unobservable).
However, I struggle intuitively to see why an AR (1) can be specified as an infinite MA process. In my own mind, a stationary AR(1) process has an autoregressive parameter which dies out and a zero-mean white noise error term.
However, I struggle to see why it is useful to convey the AR (1) in purely MA terms, if these MA terms need explained by an infinite AR in the first instance.
Would appreciate some clarity on the matter - or I hope at least it sparks some interesting conversation.