Related papers: StationarityToolkit: Comprehensive Time Series Sta…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
Stationarity transformations are standard preprocessing in time series forecasting, yet their actual impact on accuracy across different non-stationarity types and model families has received little controlled evaluation. We construct…
Traditionally stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
We introduce PyChEst, a Python package which provides tools for the simultaneous estimation of multiple changepoints in the distribution of piece-wise stationary time series. The nonparametric algorithms implemented are provably consistent…
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…
The Statistical Toolkit is an open source system specialized in the statistical comparison of distributions. It addresses requirements common to different experimental domains, such as simulation validation (e.g. comparison of experimental…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to…
We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local…
Recent advances in time-series forecasting increasingly rely on pre-trained foundation-style models. While these models often claim broad generalization, existing evaluation protocols provide limited evidence. Indeed, most current…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…
We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…
Time series forecasting is a fundamental tool with wide ranging applications, yet recent debates question whether complex nonlinear architectures truly outperform simple linear models. Prior claims of dominance of the linear model often…
Understanding the temporal properties of longitudinal data is critical for identifying trends, predicting future events, and making informed decisions in any field where temporal data is analysed, including health and epidemiology, finance,…
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…
In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximising the difference in the second-order structure over pairs of randomly drawn intervals.…
When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…