# Coupling and perturbation techniques for categorical time series

## TL;DR

This paper introduces a coupling and perturbation framework for analyzing complex categorical time series models with infinite dependence and exogenous influences, providing theoretical insights into their stationarity and dependence properties.

## Contribution

It develops a novel coupling-based approach and perturbation results for non-homogeneous chains, extending theoretical understanding of observation-driven categorical time series models.

## Key findings

- Established conditions for stationarity and ergodicity.
- Derived bounds on dependence measures.
- Provided a general theoretical framework for models in statistics and econometrics.

## Abstract

We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in the literature for bounding the relaxation speed of a chain with complete connection and from which we derive a perturbation result for non-homogenous versions of such chains. We then study stationarity, ergodicity and dependence properties of some chains with complete connections and exogenous covariates. As a consequence, we obtain a general framework for studying some observation-driven time series models used both in statistics and econometrics but without theoretical support.