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Complex data structures such as time series are increasingly present in modern data science problems. A fundamental question is whether two such time-series are statistically dependent. Many current approaches make parametric assumptions on the random processes, only detect linear association, require multiple tests, or forfeit power in high-dimensional, nonlinear settings. Estimating the distribution of any test statistic under the null is non-trivial, as the permutation test is invalid. This work juxtaposes distance correlation (Dcorr) and multiscale graph correlation (MGC) from independence testing literature and block permutation from time series analysis to address these challenges. The proposed nonparametric procedure is valid and consistent, building upon prior work by characterizing the geometry of the relationship, estimating the time lag at which dependence is maximized, avoiding the need for multiple testing, and exhibiting superior power in high-dimensional, low sample size, nonlinear settings. Neural connectivity is analyzed via fMRI data, revealing linear dependence of signals within the visual network and default mode network, and nonlinear relationships in other networks. This work uncovers a first-resort data analysis tool with open-source code available, directly impacting a wide range of scientific disciplines.
A number of universally consistent dependence measures have been recently proposed for testing independence, such as distance correlation, kernel correlation, multiscale graph correlation, etc. They provide a satisfactory solution for dependence test
Unsupervised learning seeks to uncover patterns in data. However, different kinds of noise may impede the discovery of useful substructure from real-world time-series data. In this work, we focus on mitigating the interference of left-censorship in t
Multivariate time series are routinely encountered in real-world applications, and in many cases, these time series are strongly correlated. In this paper, we present a deep learning structural time series model which can (i) handle correlated multiv
In this paper, we propose the multivariate quantile Bayesian structural time series (MQBSTS) model for the joint quantile time series forecast, which is the first such model for correlated multivariate time series to the authors best knowledge. The M
This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the time-series, Ba