{"title":"利用广义熵风险值对长记忆过程进行统计评估","authors":"Hidekazu Yoshioka, Yumi Yoshioka","doi":"10.1002/env.2838","DOIUrl":null,"url":null,"abstract":"<p>The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real-world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value-at-risk (TsVaR) as a convex risk functional to generalize the widely used entropic value-at-risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi-implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.</p>","PeriodicalId":50512,"journal":{"name":"Environmetrics","volume":"35 4","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Statistical evaluation of a long-memory process using the generalized entropic value-at-risk\",\"authors\":\"Hidekazu Yoshioka, Yumi Yoshioka\",\"doi\":\"10.1002/env.2838\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real-world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value-at-risk (TsVaR) as a convex risk functional to generalize the widely used entropic value-at-risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi-implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.</p>\",\"PeriodicalId\":50512,\"journal\":{\"name\":\"Environmetrics\",\"volume\":\"35 4\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Environmetrics\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/env.2838\",\"RegionNum\":3,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ENVIRONMENTAL SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Environmetrics","FirstCategoryId":"93","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/env.2838","RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
Statistical evaluation of a long-memory process using the generalized entropic value-at-risk
The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real-world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value-at-risk (TsVaR) as a convex risk functional to generalize the widely used entropic value-at-risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi-implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.
期刊介绍:
Environmetrics, the official journal of The International Environmetrics Society (TIES), an Association of the International Statistical Institute, is devoted to the dissemination of high-quality quantitative research in the environmental sciences.
The journal welcomes pertinent and innovative submissions from quantitative disciplines developing new statistical and mathematical techniques, methods, and theories that solve modern environmental problems. Articles must proffer substantive, new statistical or mathematical advances to answer important scientific questions in the environmental sciences, or must develop novel or enhanced statistical methodology with clear applications to environmental science. New methods should be illustrated with recent environmental data.