{"title":"Nonnegative GARCH-type models with conditional Gamma distributions and their applications","authors":"Eunju Hwang, ChanHyeok Jeon","doi":"10.1016/j.csda.2024.108006","DOIUrl":null,"url":null,"abstract":"<div><p>Most of real data are characterized by positive, asymmetric and skewed distributions of various shapes. Modelling and forecasting of such data are addressed by proposing nonnegative conditional heteroscedastic time series models with Gamma distributions. Three types of time-varying parameters of Gamma distributions are adopted to construct the nonnegative GARCH models. A condition for the existence of a stationary Gamma-GARCH model is given. Parameter estimates are discussed via maximum likelihood estimation (MLE) method. A Monte-Carlo study is conducted to illustrate sample paths of the proposed models and to see finite-sample validity of the MLEs, as well as to evaluate model diagnostics using standardized Pearson residuals. Furthermore, out-of-sample forecasting analysis is performed to compute forecasting accuracy measures. Applications to oil price and Bitcoin data are given, respectively.</p></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"198 ","pages":"Article 108006"},"PeriodicalIF":1.5000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Statistics & Data Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167947324000902","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Most of real data are characterized by positive, asymmetric and skewed distributions of various shapes. Modelling and forecasting of such data are addressed by proposing nonnegative conditional heteroscedastic time series models with Gamma distributions. Three types of time-varying parameters of Gamma distributions are adopted to construct the nonnegative GARCH models. A condition for the existence of a stationary Gamma-GARCH model is given. Parameter estimates are discussed via maximum likelihood estimation (MLE) method. A Monte-Carlo study is conducted to illustrate sample paths of the proposed models and to see finite-sample validity of the MLEs, as well as to evaluate model diagnostics using standardized Pearson residuals. Furthermore, out-of-sample forecasting analysis is performed to compute forecasting accuracy measures. Applications to oil price and Bitcoin data are given, respectively.
期刊介绍：
Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas:
I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article.
II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures.
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III) Special Applications - [...]
IV) Annals of Statistical Data Science [...]
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