论文标题
幂律相关序列的相对簇熵
Relative cluster entropy for power-law correlated sequences
论文作者
论文摘要
我们提出了一种信息理论度量，\ textit {相对群集熵} $ \ mathcal {d_ {c}} [p \ | q] $，以区分概率分布功能$ p $和$ q $的集群分区。该措施用分别带有hurst指数的分数布朗动作生成的簇$ h_1 $和$ h_2 $。对于延伸，普通和超级延伸的序列，相对熵明显取决于$ H_1 $和$ H_2 $之间的差异。通过使用\ textIt {最小相对熵}原理，可以区分以不同相关度为特征的群集序列，并选择了最佳的Hurst指数。作为一个案例研究，将市场价格序列的现实世界集群分区与假定为模型的完全不相关序列（简单的Browniam动议）进行了比较。 \ textIt {最低相对簇熵}产生最佳的Hurst指数$ H_1 = 0.55 $，$ H_1 = 0.57 $，$ H_1 = 0.63 $ = 0.63 $，DJIA，S \＆P500，NASDAQ的价格：明确指示了非杂志。最后，我们得出了相对簇熵的分析表达，并讨论了连续随机变量的幂律概率分布函数的任意成对的结果。
We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among cluster partitions characterised by probability distribution functions $P$ and $Q$. The measure is illustrated with the clusters generated by pairs of fractional Brownian motions with Hurst exponents $H_1$ and $H_2$ respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between $H_1$ and $H_2$. By using the \textit{minimum relative entropy} principle, cluster sequences characterized by different correlation degrees are distinguished and the optimal Hurst exponent is selected. As a case study, real-world cluster partitions of market price series are compared to those obtained from fully uncorrelated sequences (simple Browniam motions) assumed as a model. The \textit{minimum relative cluster entropy} yields optimal Hurst exponents $H_1=0.55$, $H_1=0.57$, and $H_1=0.63$ respectively for the prices of DJIA, S\&P500, NASDAQ: a clear indication of non-markovianity. Finally, we derive the analytical expression of the relative cluster entropy and the outcomes are discussed for arbitrary pairs of power-laws probability distribution functions of continuous random variables.
