{"title":"Modeling Z-valued time series based on new versions of the Skellam INGARCH model","authors":"Yan Cui, Qi Li, Fukang Zhu","doi":"10.1214/20-BJPS473","DOIUrl":null,"url":null,"abstract":"Recently, there has been a growing interest in integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, but only a few of them can deal with data on the full set of integers, i.e., Z = {...,−2,−1, 0, 1, 2, ...}. Although some attempts have been made to deal with Z-valued time series, these models do not provide enough flexibility in modeling some specific integers (e.g. 0, ±1). A symmetric Skellam INGARCH(1,1) model was proposed in the literature, but it only considered zero-mean processes, which limits its application. We first extend the symmetric Skellam INGARCH model to an asymmetric version, which can deal with non-zero-mean processes. Then we propose a modified Skellam model which adopts a careful treatment on integers 0 and ±1 to satisfy a special feature of the data. Our models are easy-to-use and flexible. The maximum likelihood method is used to estimate unknown parameters and the log-likelihood ratio test statistic is provided for testing the asymmetric model against the modified one. Simulation studies are given to evaluate performances of the parametric estimation and log-likelihood ratio test. A real data example is also presented to demonstrate good performances of newly proposed models.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/20-BJPS473","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 9
Abstract
Recently, there has been a growing interest in integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, but only a few of them can deal with data on the full set of integers, i.e., Z = {...,−2,−1, 0, 1, 2, ...}. Although some attempts have been made to deal with Z-valued time series, these models do not provide enough flexibility in modeling some specific integers (e.g. 0, ±1). A symmetric Skellam INGARCH(1,1) model was proposed in the literature, but it only considered zero-mean processes, which limits its application. We first extend the symmetric Skellam INGARCH model to an asymmetric version, which can deal with non-zero-mean processes. Then we propose a modified Skellam model which adopts a careful treatment on integers 0 and ±1 to satisfy a special feature of the data. Our models are easy-to-use and flexible. The maximum likelihood method is used to estimate unknown parameters and the log-likelihood ratio test statistic is provided for testing the asymmetric model against the modified one. Simulation studies are given to evaluate performances of the parametric estimation and log-likelihood ratio test. A real data example is also presented to demonstrate good performances of newly proposed models.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
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(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.