Separation of components from a scale mixture of Gaussian white noises.
Separation of components from a scale mixture of Gaussian white noises.
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从高斯白噪声的比例混合中分离成分。
DOI：
10.1103/physreve.81.051125
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Craciun
中科院分区：
文献类型：
--
作者：
C. Vamos;M. Craciun
与热力学系统相关的物理量的时间演化，其平衡波动的幅度由缓慢变化的现象调制，可以建模为高斯白噪声{zt}和具有严格正值的随机过程{vt}的乘积，称为波动。过程X t =V t Z t的概率密度函数（pdf）是高斯白噪声的尺度混合，表示为由波动率pdf加权的高斯分布的时间平均值。{X t}的两个分量的分离可以通过施加估计白噪声的绝对值不相关的条件来实现。我们将这种方法应用于标准普尔500指数的每日收益的时间序列，也通过施加估计白噪声为高斯的条件的超统计方法进行了分析。我们的方法的优点是，该金融时间序列的处理没有分割或去除极端事件，估计的白噪声几乎成为高斯仅作为不相关条件的结果。
The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Z t} and a stochastic process with strictly positive values {V t} referred to as volatility. The probability density function (pdf) of the process X t =V t Z t is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {X t} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.