This article serves two purposes. Firstly, it surveys the Bandt and Pompe methodology for the statistical community, stressing topics that are open for research. Secondly, it contributes towards a better understanding of the statistical properties of that approach for time series analysis. The Bandt and Pompe methodology consists of computing information theory descriptors from the histogram of ordinal patterns. Such descriptors lie in a 2D manifold: the entropy–complexity plane. This article provides the first proposal of a test in the entropy–complexity plane for the white noise hypothesis. Our test is based on true white noise sequences obtained from physical devices. The proposed methodology provides consistent results: It assesses sequences of true random samples as random (adequate test size), rejects correlated and contaminated sequences (sound test power) and captures the randomness of generators previously analysed in the literature.

中文翻译：

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熵-复杂平面中序数模式的白噪声测试

本文有两个目的。首先，它调查了统计界的 Bandt 和 Pompe 方法，强调了可供研究的主题。其次，它有助于更​​好地理解时间序列分析方法的统计特性。Bandt 和 Pompe 方法包括从序数模式的直方图中计算信息论描述符。这样的描述符位于二维流形中：熵-复杂度平面。本文为白噪声假设提供了熵-复杂性平面中的测试的第一个提议。我们的测试基于从物理设备获得的真实白噪声序列。所提出的方法提供了一致的结果：它将真实随机样本的序列评估为随机（足够的测试规模），