Comments on the presence of serial correlation in the random coefficients of an autoregressive process

TL;DR

This paper investigates the impact of serial correlation in the coefficients of an RCAR(p) process, revealing that standard estimators become inconsistent under such conditions and providing the correct asymptotic analysis.

Contribution

It demonstrates the inconsistency of standard estimators in RCAR(p) processes with serially correlated coefficients and derives their correct asymptotic behavior.

Findings

Standard estimators are inconsistent with serial correlation in coefficients.

The paper provides the correct asymptotic behavior of estimators.

Simulations illustrate the theoretical results.

Abstract

We consider an RCAR$(p)$ process and we establish that the standard estimation lacks consistency as soon as there exists a nonzero serial correlation in the coefficients. We give the correct asymptotic behavior and some simulations come to illustrate the results.