# Necessary and sufficient conditions for the identifiability of observation-driven models

## TL;DR

This paper establishes necessary and sufficient conditions for the identifiability of observation-driven models, including GARCH and integer-valued time series models, ensuring the consistency of estimators.

## Contribution

It extends the identifiability conditions from GARCH models to a broader class called linearly observation-driven models, covering various standard time series models.

## Key findings

- Identifiability conditions are established for a broad class of models.
- Conditions ensure the consistency of quasi-maximum likelihood estimators.
- Includes standard models like Poisson GARCH and NBIN-GARCH.

## Abstract

In this contribution we are interested in proving that a given observation-driven model is identifiable. In the case of a GARCH(p, q) model, a simple sufficient condition has been established in [1] for showing the consistency of the quasi-maximum likelihood estimator. It turns out that this condition applies for a much larger class of observation-driven models, that we call the class of linearly observation-driven models. This class includes standard integer valued observation-driven time series, such as the log-linear Poisson GARCH or the NBIN-GARCH models.