Testing for the extent of instability in nearly unstable processes

Author:

Badreau Marie1ORCID,Proïa Frédéric2ORCID

Affiliation:

1. Laboratoire Manceau de Mathématiques Le Mans Université Le Mans France

2. Univ Angers, CNRS, LAREMA, SFR MATHSTIC Angers France

Abstract

This article deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to autoregressive processes where the bridge between stability and instability is expressed by means of time‐varying coefficients. The process we consider has a companion matrix with spectral radius satisfying , a situation described as ‘nearly‐unstable’. The question we investigate is: given an observed path supposed to come from a nearly unstable process, is it possible to test for the ‘extent of instability’, i.e. to test how close we are to the unit root? In this regard, we develop a strategy to evaluate and to test for : ‘’ against : ‘’ when lies in an inner ‐neighborhood of the unity, for some . Empirical evidence is given about the advantages of the flexibility induced by such a procedure compared to the common unit root tests. We also build a symmetric procedure for the usually left out situation where the dominant root lies around .

Funder

Agence Nationale de la Recherche

Publisher

Wiley

Reference35 articles.

1. Consistency and asymptotic normality in a class of nearly unstable processes;Badreau M;Statistical Inference for Stochastic Processes,2023

2. Asymptotic behavior of unstable INARp processes;Barczy M;Stochastic Processes and their Applications,2011

3. Nearly unstable integer‐valued ARCH process and unit root testing;Barreto‐Souza W;Scandinavian Journal of Statistics,2024

4. On the theory of testing for unit roots in observed time series;Bhargava A;The Review of Economic Studies,1986

5. Springer Series in Statistics;Brockwell PJ,1991

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3