{"title":"Optimal estimating function for weak location-scale dynamic models","authors":"Christian Francq, Jean-Michel Zakoïan","doi":"10.1111/jtsa.12684","DOIUrl":null,"url":null,"abstract":"<p>Estimating functions provide a very general framework for the statistical inference of dynamic models under weak assumptions. We consider a class of time series models consisting in the parametrization of the first two conditional moments which – by contrast with classical location-scale dynamic models – do not impose further constraints on the conditional distribution/moments. Quasi-likelihood estimators (QLE) are obtained by solving estimating equations deduced from those two conditional moments. Conditions ensuring the existence and asymptotic properties (consistency and asymptotic normality) of such estimators are provided. We propose optimal QLEs in Godambe's sense, deduced from a condition obtained by Chandra and Taniguchi (2001, <i>Annals of the Institute of Statistical Mathematics</i> 53, 125–141). The particular case of the quasi-maximum likelihood estimators is considered. For pure location models, a data-driven procedure for optimally choosing the QLE is proposed. Our results are illustrated via Monte Carlo experiments and real financial data.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 5-6","pages":"533-555"},"PeriodicalIF":1.2000,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Time Series Analysis","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12684","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
Estimating functions provide a very general framework for the statistical inference of dynamic models under weak assumptions. We consider a class of time series models consisting in the parametrization of the first two conditional moments which – by contrast with classical location-scale dynamic models – do not impose further constraints on the conditional distribution/moments. Quasi-likelihood estimators (QLE) are obtained by solving estimating equations deduced from those two conditional moments. Conditions ensuring the existence and asymptotic properties (consistency and asymptotic normality) of such estimators are provided. We propose optimal QLEs in Godambe's sense, deduced from a condition obtained by Chandra and Taniguchi (2001, Annals of the Institute of Statistical Mathematics 53, 125–141). The particular case of the quasi-maximum likelihood estimators is considered. For pure location models, a data-driven procedure for optimally choosing the QLE is proposed. Our results are illustrated via Monte Carlo experiments and real financial data.
期刊介绍:
During the last 30 years Time Series Analysis has become one of the most important and widely used branches of Mathematical Statistics. Its fields of application range from neurophysiology to astrophysics and it covers such well-known areas as economic forecasting, study of biological data, control systems, signal processing and communications and vibrations engineering.
The Journal of Time Series Analysis started in 1980, has since become the leading journal in its field, publishing papers on both fundamental theory and applications, as well as review papers dealing with recent advances in major areas of the subject and short communications on theoretical developments. The editorial board consists of many of the world''s leading experts in Time Series Analysis.