Related papers: Asymptotic spectral theory for nonlinear time seri…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
A fully nonlinear, time-asymptotic theory of resonant particle trapping in large-amplitude quasi-parallel Alfven waves is presented. The effect of trapped particles on the nonlinear dynamics of quasi-stationary Alfvenic discontinuities and…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…
In this article, we propose a spectral method for a class of multivariate inhomogeneous spatial point processes, namely the second-order intensity reweighted stationary processes. A key ingredient of our approach is utilizing the asymptotic…
This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…
We introduce the concept of phase-synchronous undersampling in nonlinear spectroscopy. The respective theory is presented and validated experimentally in a phase-modulated quantum beat experiment by sampling high phase modulation…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…
In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…
We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…