Related papers: Statistical Test for Dynamical Nonstationarity in …
Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
A common assumption in the spatial analysis of agricultural field trials is stationarity. In practice, however, this assumption is often violated due to unaccounted field effects. For instance, in plant breeding field trials, this can lead…
Basin stability (BS) is a measure of nonlinear stability in multi-stable dynamical systems. BS has previously been estimated using Monte-Carlo simulations, which requires the explicit knowledge of a dynamical model. We discuss the…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
We derive tests of stationarity for univariate time series by combining change-point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a…
Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For…
We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown…
Time-of-flight measurements such as the OPERA and MINOS experiments rely crucially on statistical analysis (as well as many other ingredients) for their conclusions. The nature of these experiments leads to a simple class of statistical…
This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…