{"title":"On higher-order moments of INGARCH processes","authors":"Christian H. Weiß","doi":"10.1016/j.spl.2024.110198","DOIUrl":null,"url":null,"abstract":"<div><p>For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the <span><math><mi>k</mi></math></span>th factorial moment is proportional to the <span><math><mi>k</mi></math></span>th power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"214 ","pages":"Article 110198"},"PeriodicalIF":0.9000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001676/pdfft?md5=1a05e917c26685be8f2bdbd5ed320859&pid=1-s2.0-S0167715224001676-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224001676","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
For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the th factorial moment is proportional to the th power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.
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