{"title":"分类时间序列的加权离散 ARMA 模型","authors":"Christian H. Weiß, Osama Swidan","doi":"10.1111/jtsa.12773","DOIUrl":null,"url":null,"abstract":"A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and ‐mixing solution as well as closed‐form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite‐sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real‐world data application.","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"68 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weighted discrete ARMA models for categorical time series\",\"authors\":\"Christian H. Weiß, Osama Swidan\",\"doi\":\"10.1111/jtsa.12773\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and ‐mixing solution as well as closed‐form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite‐sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real‐world data application.\",\"PeriodicalId\":49973,\"journal\":{\"name\":\"Journal of Time Series Analysis\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Time Series Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1111/jtsa.12773\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Time Series Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1111/jtsa.12773","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Weighted discrete ARMA models for categorical time series
A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and ‐mixing solution as well as closed‐form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite‐sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real‐world data application.
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.