Related papers: Empirical process theory for locally stationary pr…

Causal inference from observational data following the restricted structural causal models (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

Observing a load process above high thresholds, modeling it as a pulse process with random occurrence times and magnitudes, and extrapolating life-time maximum or design loads from the data is a common task in structural reliability…

In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…

This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…

We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the…

We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass.…

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…

We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…

We study the statistical inference of nonlinear stochastic approximation algorithms utilizing a single trajectory of Markovian data. Our methodology has practical applications in various scenarios, such as Stochastic Gradient Descent (SGD)…

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…

Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size,…

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…

We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…

Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…

We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…