Related papers: Probability inequalities for high dimensional time…

Assessing the predictive power of both data and models holds paramount significance in time-series machine learning applications. Yet, preparing time series data accurately and employing an appropriate measure for predictive power seems to…

High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…

The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the…

Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…

The success of large-scale models in recent years has increased the importance of statistical models with numerous parameters. Several studies have analyzed over-parameterized linear models with high-dimensional data, which may not be…

This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

High-dimensional time series are characterized by a large number of measurements and complex dependence, and often involve abrupt change points. We propose a new procedure to detect change points in the mean of high-dimensional time series…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…

In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…