{"title":"Specifications tests for count time series models with covariates","authors":"Šárka Hudecová, Marie Hušková, Simos G. Meintanis","doi":"10.1007/s11749-024-00933-x","DOIUrl":null,"url":null,"abstract":"<p>We propose a goodness-of-fit test for a class of count time series models with covariates which includes the Poisson autoregressive model with covariates (PARX) as a special case. The test criteria are derived from a specific characterization for the conditional probability generating function, and the test statistic is formulated as a <span>\\(L_2\\)</span> weighting norm of the corresponding sample counterpart. The asymptotic properties of the proposed test statistic are provided under the null hypothesis as well as under specific alternatives. A bootstrap version of the test is explored in a Monte–Carlo study and illustrated on a real data set on road safety.\n</p>","PeriodicalId":51189,"journal":{"name":"Test","volume":"193 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Test","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11749-024-00933-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a goodness-of-fit test for a class of count time series models with covariates which includes the Poisson autoregressive model with covariates (PARX) as a special case. The test criteria are derived from a specific characterization for the conditional probability generating function, and the test statistic is formulated as a \(L_2\) weighting norm of the corresponding sample counterpart. The asymptotic properties of the proposed test statistic are provided under the null hypothesis as well as under specific alternatives. A bootstrap version of the test is explored in a Monte–Carlo study and illustrated on a real data set on road safety.
期刊介绍：
TEST is an international journal of Statistics and Probability, sponsored by the Spanish Society of Statistics and Operations Research. English is the official language of the journal.
The emphasis of TEST is placed on papers containing original theoretical contributions of direct or potential value in applications. In this respect, the methodological contents are considered to be crucial for the papers published in TEST, but the practical implications of the methodological aspects are also relevant. Original sound manuscripts on either well-established or emerging areas in the scope of the journal are welcome.
One volume is published annually in four issues. In addition to the regular contributions, each issue of TEST contains an invited paper from a world-wide recognized outstanding statistician on an up-to-date challenging topic, including discussions.
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