论文标题
比较固定框架中Hurst指数估算的最大似然和绝对时刻
A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework
论文作者
论文摘要
绝对时刻的方法是估计分数布朗尼$ x $的赫斯特指数的普遍方法。但是，当应用于$ x $的固定版本时，这种方法会偏向$ x $，尤其是$ x $的逆向lamperti变换，线性时间收缩为$θ$。我们提出了绝对时刻方法的改编，并将其与最大似然方法进行比较，并将其与仿真和对财务时间序列的应用程序进行了比较。虽然看来最大样本方法比适应的绝对时音估计更准确，但最后一个方法并不兴趣，这有两个原因：可以直观地确认该模型已很好地指定了模型，并且在计算上的性能更高。
The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion $X$. But this method is biased when applied to a stationary version of $X$, in particular an inverse Lamperti transform of $X$, with a linear time contraction of parameter $θ$. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations and an application to a financial time series. While it appears that the maximum-likelihood method is more accurate than the adapted absolute-moment estimation, this last method is not uninteresting for two reasons: it makes it possible to confirm visually that the model is well specified and it is computationally more performing.
