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We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…
The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series,…
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
The time-frequency map (TFM) is frequently used in condition monitoring, necessitating further processing to select an informative frequency band (IFB) or directly detect damage. However, selecting an IFB is challenging due to the…
Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph…
We present an analysis of the non-Gaussianity in the distribution of Ly$\alpha$ forest lines in the QSO absorption spectra. Statistical tests performed on this data indicate that there may be large scale structure even though the power…
Local regression is widely used to explore spatial heterogeneity, but anisotropic or effectively low-dimensional neighborhoods can produce ill-conditioned local solves, causing coefficient variation driven by numerical artifacts rather than…
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…
We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of their (discrete) spectra, in the semiclassical limit $h\to 0$.…
We review the advancement of nonstationary time series analysis from the perspective of Cowles Commission structural equation approach. We argue that despite the rich repertoire nonstationary time series analysis provides to analyze how do…
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the…
Financial spillovers in interconnected systems, such as global banking networks, require tools that capture temporal and frequency dynamics, while incorporating the underlying network topology. While current network time series models are…
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…