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 robust 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.

翻译：无尺度动力学通过自相似性形式化，为真实世界数据中的时间动态建模提供了一种广泛使用的通用范式。然而，其实际应用至今仍主要局限于单变量场景。相比之下，现代应用往往要求进行多变量数据分析。为此，近期提出了多元自相似性模型。然而，由于缺乏对自相似性参数向量的稳健估计方法，这些模型在实践中仍鲜少被应用。基于最新的数学进展，本研究提出了一种高效的估计方法，该方法通过对多元自相似过程小波谱的多尺度特征结构进行理论分析而建立。估计性能在大尺度与样本容量的渐近极限下进行了理论分析，并对有限样本进行了计算验证。作为实践成果，一个功能完备且附有文档说明的多元信号处理估计工具包已免费开放，可直接应用于真实世界数据。其在多通道脑电图数据的癫痫发作预测中的潜在优势得到了实例验证。