Scale-free dynamics, formalized by selfsimilarity, provides a versatile paradigm massively and ubiquitously used to model temporal dynamics in real-world data. However, its practical use has mostly remained univariate so far. By contrast, modern applications often demand multivariate data analysis. Accordingly, models for multivariate selfsimilarity were recently proposed. Nevertheless, they have remained rarely used in practice because of a lack of available reliable estimation procedures for the vector of selfsimilarity parameters. Building upon recent mathematical developments, the present work puts forth an efficient estimation procedure based on the theoretical study of the multiscale eigenstructure of the wavelet spectrum of multivariate selfsimilar processes. The estimation performance is studied theoretically in the asymptotic limits of large scale and sample sizes, and computationally for finite-size samples. As a practical outcome, a fully operational and documented multivariate signal processing estimation toolbox is made freely available and is ready for practical use on real-world data. Its potential benefits are illustrated in epileptic seizure prediction from multi-channel EEG data.

中文翻译：

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多元自相似性：自相似参数估计的多尺度特征结构


通过自相似性形式化的无标度动力学提供了一种广泛且普遍用于模拟现实世界数据中的时间动态的通用范例。然而，迄今为止，其实际用途大多仍是单变量。相比之下，现代应用程序通常需要多元数据分析。因此，最近提出了多元自相似性模型。然而，由于缺乏自相似参数向量的可用可靠估计程序，它们在实践中仍然很少使用。基于最近的数学发展，本工作提出了一种基于多元自相似过程小波谱的多尺度本征结构的理论研究的有效估计程序。从理论上研究了大尺度和样本量的渐近极限下的估计性能，并在计算上研究了有限大小样本的估计性能。作为一个实际成果，一个完全可操作且有记录的多元信号处理估计工具箱免费提供，并准备好在现实世界数据上实际使用。它的潜在好处在多通道脑电图数据的癫痫发作预测中得到了说明。