Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes

TL;DR

This paper proves that for short-memory processes like ARMA, the exponential decay rate of partial autocorrelation coefficients matches that of the infinite autoregressive coefficients, providing a concise proof of this property.

Contribution

It offers a short, elegant proof establishing the equality of decay rates for partial autocorrelation and AR coefficients in short-memory processes.

Findings

Decay rate of partial autocorrelation equals that of AR coefficients

Short proof provided for the decay rate equivalence

Applicable to ARMA and similar short-memory processes

Abstract

We present a short proof of the fact that the exponential decay rate of partial autocorrelation coefficients of a short-memory process, in particular an ARMA process, is equal to the exponential decay rate of the coefficients of its infinite autoregressive representation.