几何布朗运动的拟合优度检验

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2025-04-23 DOI:10.1016/j.csda.2025.108196

Daniel Gaigall , Philipp Wübbolding

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引用次数: 0

摘要

在函数数据集中，研究了数据来源于几何布朗运动的复合零假设的拟合优度检验。这相当于测试数据是否来自线性漂移的布朗运动。获得测试的临界值，确保在有限样本中达到指定的显著性水平。研究了检验统计量在零分布和备选项下的渐近性，并证明了检验量是一致的。此外，所提出的方法在快速和简单的实现方面具有优势。综合仿真研究表明，新方法的性能优于现有方法。一个关键的应用是评估金融时间序列对布莱克-斯科尔斯模型的适用性。为了说明所提出的测试，给出了与各种股票和利率时间序列有关的示例。

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A goodness-of-fit test for geometric Brownian motion

A new goodness-of-fit test for the composite null hypothesis that data originate from a geometric Brownian motion is studied in the functional data setting. This is equivalent to testing if the data are from a scaled Brownian motion with linear drift. Critical values for the test are obtained, ensuring that the specified significance level is achieved in finite samples. The asymptotic behavior of the test statistic under the null distribution and alternatives is studied, and it is also demonstrated that the test is consistent. Furthermore, the proposed approach offers advantages in terms of fast and simple implementation. A comprehensive simulation study shows that the power of the new test compares favorably to that of existing methods. A key application is the assessment of financial time series for the suitability of the Black-Scholes model. Examples relating to various stock and interest rate time series are presented in order to illustrate the proposed test.

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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 [...]