Nonnegative GARCH-type models with conditional Gamma distributions and their applications

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2024-06-13 DOI:10.1016/j.csda.2024.108006

Eunju Hwang, ChanHyeok Jeon

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.

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具有条件伽马分布的非负 GARCH 型模型及其应用

大多数真实数据都具有正分布、非对称分布和各种形状的倾斜分布。针对这类数据的建模和预测，提出了伽玛分布的非负条件异方差时间序列模型。在构建非负 GARCH 模型时，采用了 Gamma 分布的三种时变参数。给出了静态 Gamma-GARCH 模型的存在条件。通过最大似然估计（MLE）方法讨论了参数估计。进行了蒙特卡洛研究，以说明所提模型的样本路径，了解 MLE 的有限样本有效性，并使用标准化皮尔逊残差对模型诊断进行评估。此外，还进行了样本外预测分析，以计算预测准确度。分别给出了石油价格和比特币数据的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

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. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]