A goodness-of-fit test for geometric Brownian motion
提出一种新的拟合优度检验，判断数据是否来自几何布朗运动，适用于评估金融时间序列是否符合布莱克-舒尔斯模型，模拟显示检验功效优于现有方法。
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.