Related papers: StationarityToolkit: Comprehensive Time Series Sta…

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…

Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal…

The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to…

Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over…

Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…

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…

The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal…

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique,…

PyPOTS is an open-source Python library dedicated to data mining and analysis on multivariate partially-observed time series with missing values. Particularly, it provides easy access to diverse algorithms categorized into five tasks:…

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…

We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

The danger of confusing long-range dependence with non-stationarity has been pointed out by many authors. Finding an answer to this difficult question is of importance to model time-series showing trend-like behavior, such as river run-off…

This paper presents a practical approach for detecting non-stationarity in time series prediction. This method is called SAFE and works by monitoring the evolution of the spectral contents of time series through a distance function. This…

Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with,…

Time series modeling for predictive purpose has been an active research area of machine learning for many years. However, no sufficiently comprehensive and meanwhile substantive survey was offered so far. This survey strives to meet this…

Nonstationarity of the event rate is a persistent problem in modeling time series of events, such as neuronal spike trains. Motivated by a variety of patterns in neurophysiological spike train recordings, we define a general class of…

Detecting anomalies in time series data is a challenging task with broad relevance in many applications. Existing methods work effectively only under idealized conditions, typically focusing on point anomalies or assuming a constant…