Necessary and Sufficient Condition for Nonsingular Fisher Information Matrix in ARMA Models

TL;DR

This paper establishes that an ARMA model's Fisher information matrix is nonsingular if and only if the model is non-redundant, meaning its AR and MA polynomials do not share roots, clarifying conditions for model identifiability.

Contribution

It provides a precise necessary and sufficient condition for the nonsingularity of the Fisher information matrix in ARMA models, linking it to the non-redundancy of the model.

Findings

Fisher information matrix is nonsingular iff AR and MA polynomials have no common roots.

Clarifies the condition for model identifiability in ARMA models.

Provides theoretical foundation for parameter estimation stability.

Abstract

It is demonstrated that a necessary and sufficient condition that the Fisher information matrix of an ARMA model be nonsingular is that the model not be redundant, that is, the autoregressive and moving-average polynomials do not share common roots.