# Testing for strict stationarity in a random coefficient autoregressive model

## TL;DR

This paper introduces a versatile statistical test for determining strict stationarity versus non-stationarity in Random Coefficient AutoRegression models, applicable even with infinite variance and minimal assumptions.

## Contribution

It develops a novel randomized diagnostic and test procedure that works broadly, including for standard AR(1) models and cases with infinite variance, without prior knowledge or modifications.

## Key findings

- Test diverges under null hypothesis
- Test drifts to zero under alternative hypothesis
- Applicable to models with infinite variance

## Abstract

We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of non-stationarity, in the context of a Random Coefficient AutoRegression (RCAR). The procedure is based on randomising a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomised test which can be used directly and - building on it - a decision rule to discern between the null and the alternative. The procedure can be applied under very general circumstances: albeit developed for an RCAR model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments.