具有漂移和平稳增量的标度不变过程的Hurst估计
Hurst estimation of scale invariant processes with drift and stationary increments
摘要：
离散尺度不变（DSI）过程的特征是其有限维分布对一定尺度因子的伸缩不变性。引入并研究了具有分段线性漂移和固定增量的DSI过程。为了识别过程的结构，首先我们确定标度区间及其线性漂移并消除它们。然后提出了一种新的方法来估计这类DSI过程的Hurst参数，并将其应用于道琼斯指数的某些时段。该方法基于连续尺度区间内的固定数量的等距样本。我们还提出了一些估计具有平稳增量的自相似过程的Hurst参数的有效方法。用分数布朗运动的模拟数据比较了该方法与著名的FA、DFA和DMA的性能。
英文摘要：
The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first we determine the scale intervals, their linear drifts and eliminate them. Then a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion.
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