Yamashita Rios de Sousa Arthur Matsuo, Takayasu Hideki, Takayasu Misako
Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan.
Institute of Innovative Research, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan.
Entropy (Basel). 2018 Jul 7;20(7):511. doi: 10.3390/e20070511.
We use the definition of statistical symmetry as the invariance of a probability distribution under a given transformation and apply the concept to the underlying probability distribution of stochastic processes. To measure the degree of statistical asymmetry, we take the Kullback-Leibler divergence of a given probability distribution with respect to the corresponding transformed one and study it for the Gaussian autoregressive process using transformations on the temporal correlations' structure. We then illustrate the employment of this notion as a time series analysis tool by measuring local statistical asymmetries of foreign exchange market price data for three transformations that capture distinct autocorrelation behaviors of the series-independence, non-negative correlations and Markovianity-obtaining a characterization of price movements in terms of each statistical symmetry.
我们将统计对称性定义为概率分布在给定变换下的不变性，并将该概念应用于随机过程的基础概率分布。为了衡量统计不对称程度，我们计算给定概率分布相对于相应变换后的概率分布的库尔贝克-莱布勒散度，并使用对时间相关性结构的变换来研究高斯自回归过程的这种散度。然后，我们通过测量外汇市场价格数据的局部统计不对称性，来说明这个概念作为时间序列分析工具的应用，这三种变换分别捕捉了该序列的不同自相关行为——独立性、非负相关性和马尔可夫性——从而根据每种统计对称性得到价格走势的特征描述。
