{"title":"Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors","authors":"Bing Su, Fu-kang Zhu, Ju Huang","doi":"10.1007/s10255-023-1096-x","DOIUrl":null,"url":null,"abstract":"<div><p>The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"39 4","pages":"972 - 989"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1096-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.