Related papers: Locally Stationary Functional Time Series
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in…
The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
We study the impact of the recently introduced underspread/overspread classificationon the spectra of processes with square-integrable covariance functions. We briefly review the most prominent definitions of a time-varying power spectrum…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…
Frequently econometricians are interested in verifying a relationship between two or more time series. Such analysis is typically carried out by causality and/or independence tests which have been well studied when the data is univariate or…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
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…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
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 the class of ARCH$(\infty)$ models is generalized to the nonstationary class of ARCH$(\infty)$ models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation ``locally…
We study distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint…
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…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…
Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…