Good day!
I'm reading about autoregressive models and would appreciate some help in understanding/interpreting the maths from the text that is in attachment (Time Series Analysis by Box and Jenkins).
When explaining why the autoregressive model is a special case of a linear filter model, we do m successive substitutions in a simple first-order autoregressive process (p = 1) and we obtain a series representation. I get where the exponentials >1 come from: the arithmetics of the substitutions, but I don't understand its real-life meaning.
I feel this is related to the stationarity explanation and the autoregressive operator considered as a polynomial in B (the backward shift operator) of degree p, but I don't really see it. How could we get the roots of this operator? Numerically, how would an operator like this look like? How could we check for the absolute value of the operator?
I appreciate any light you could provide me with!
I'm reading about autoregressive models and would appreciate some help in understanding/interpreting the maths from the text that is in attachment (Time Series Analysis by Box and Jenkins).
When explaining why the autoregressive model is a special case of a linear filter model, we do m successive substitutions in a simple first-order autoregressive process (p = 1) and we obtain a series representation. I get where the exponentials >1 come from: the arithmetics of the substitutions, but I don't understand its real-life meaning.
I feel this is related to the stationarity explanation and the autoregressive operator considered as a polynomial in B (the backward shift operator) of degree p, but I don't really see it. How could we get the roots of this operator? Numerically, how would an operator like this look like? How could we check for the absolute value of the operator?
I appreciate any light you could provide me with!
