Editing Autoregressive model (section)

==Characteristic polynomial==
The [[autocorrelation function]] of an AR(''p'') process can be expressed as {{Citation needed|date=October 2011|reason=a_k not defined and seems wrong}}
:<math>\rho(\tau) = \sum_{k=1}^p a_k y_k^{-|\tau|} ,</math>

where <math>y_k</math> are the roots of the polynomial
: <math>\phi(B) = 1- \sum_{k=1}^p \varphi_k B^k </math>

where ''B'' is the [[backshift operator]], where <math>\phi(\cdot)</math> is the function defining the autoregression, and where <math>\varphi_k</math> are the coefficients in the autoregression. The formula is valid only if all the roots have multiplicity 1.{{Citation needed|date=July 2022|reason=it is true but needs reference, see talk page}}

The autocorrelation function of an AR(''p'') process is a sum of decaying exponentials.
* Each real root contributes a component to the autocorrelation function that decays exponentially.
* Similarly, each pair of complex conjugate roots contributes an exponentially damped oscillation.