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英文文献：The Confidence Limits of a Geometric Brownian Motion-几何布朗运动的置信极限
英文文献作者：Turvey, Calum G.,Power, Gabriel J.
英文文献摘要：
This paper investigates whether the assumption of Brownian motion often used to describe commodity price movements is satisfied. Using historical data from 17 commodity futures contracts specific tests of fractional and ordinary Brownian motion are conducted. The analyses are conducted under the null hypothesis of ordinary Brownian motion against the alternative of persistent or ergodic fractional Brownian motion. Tests for fractional Brownian motion are based on a variance ratio test. However, standard errors based on Monte Carlo simulations are quite high, meaning that the acceptance region for the null hypothesis is large. The results indicate that for the most part, the null hypothesis of ordinary Brownian motion cannot be rejected for 14 of 17 series. The three series that did not satisfy the tests were rejected because they violated the stationarity property of the random walk hypothesis.
摘要本文研究了常用的描述商品价格变动的布朗运动假设是否满足。利用17个商品期货合约的历史数据，对部分布朗运动和普通布朗运动进行了具体的检验。在一般布朗运动的零假设下，对持续或遍历分式布朗运动的选择进行了分析。分数布朗运动的检验是基于方差比检验。然而，基于蒙特卡洛模拟的标准误差相当高，这意味着零假设的接受区域很大。结果表明，在大多数情况下，在17个系列中的14个中，普通布朗运动的零假设是不能被拒绝的。三个不满足检验的序列被拒绝，因为它们违反了随机游走假设的平稳性。
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