{"title":"Time changes and stationarity issues for extended scalar autoregressive models","authors":"V. Girardin , R. Senoussi","doi":"10.1016/j.jspi.2023.106112","DOIUrl":null,"url":null,"abstract":"<div><p>A scalar discrete or continuous time process is reducible to stationarity (RWS) if its transform by some smooth time change is weakly stationary. Different issues linked to this notion are here investigated for autoregressive (AR) models. AR models are understood in a large sense and may have time-varying coefficients. In the continuous time case the innovation may be of the semi-martingale type–such as compound Poisson noise; in the discrete case, the noise may not be Gaussian.</p><p>Necessary and sufficient conditions for scalar AR models to be RWS are investigated, with explicit formulas for the time changes. Stationarity reduction issues for discrete sequences sampled from time continuous AR processes are also considered. Several types of time changes, RWS processes and sequences are studied with examples and simulation, including the classical multiplicative stationary AR models.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375823000812","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
A scalar discrete or continuous time process is reducible to stationarity (RWS) if its transform by some smooth time change is weakly stationary. Different issues linked to this notion are here investigated for autoregressive (AR) models. AR models are understood in a large sense and may have time-varying coefficients. In the continuous time case the innovation may be of the semi-martingale type–such as compound Poisson noise; in the discrete case, the noise may not be Gaussian.
Necessary and sufficient conditions for scalar AR models to be RWS are investigated, with explicit formulas for the time changes. Stationarity reduction issues for discrete sequences sampled from time continuous AR processes are also considered. Several types of time changes, RWS processes and sequences are studied with examples and simulation, including the classical multiplicative stationary AR models.
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The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists.
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