论文标题
单变量时间序列中订单模式的统计和建模
Statistics and modelling of order patterns in univariate time series
论文作者
论文摘要
由于平稳性的假设最少，订单模式非常适用于许多领域。在这里，我们通过引入四个模式对比度的正交系统来修复长度3模式的方法。这些对比在统计上是独立的，并且在独立模型和随机步行模型中都是协方差矩阵的特征向量。最重要的对比是转弯率。它可用于直接从脑电图数据中评估睡眠深度。本文讨论了置换熵的波动，统计测试以及诸如脑电图之类的噪音的新模型的需求。我们展示了如何在没有任何数值值的情况下构建序数固定过程。通过扔硬币的订单是一个自然的例子。长度$ m $的图案上的每个部分固定的概率度量都可以扩展到无限长度模式的固定度量。
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically independent and turn up as eigenvectors of a covariance matrix both in the independence model and the random walk model. The most important contrast is turning rate. It can be used to evaluate sleep depth directly from EEG data. The paper discusses fluctuations of permutation entropy, statistical tests, and the need of new models for noises like EEG. We show how ordinal stationary processes can be constructed without any numerical values. An order by coin-tossing is a natural example. Every partially stationary probability measure on patterns of length $m$ can be extended to a stationary measure on patterns of infinite length.
