Related papers: StationarityToolkit: Comprehensive Time Series Sta…

The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

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…

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation…

A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically…

Very large time series are increasingly available from an ever wider range of IoT-enabled sensors, from which significant insights can be obtained through mining temporal patterns from them. A useful type of patterns found in many…

Seasonality (or periodicity) and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is not an easy task for existing methods to analyze…

We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general…

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot…

We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z…

This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…

The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing…

The aim of this paper is to give a presentation of the Python toolbox YALTAPy dedicated to the stability study of standard and fractional delay systems as well as its online version YALTAPy_Online. Both toolboxes are derived from YALTA…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model…

Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal…

We introduce BASTION (Bayesian Adaptive Seasonality and Trend DecompositION), a flexible Bayesian framework for decomposing time series into trend and multiple seasonality components. We cast the decomposition as a penalized nonparametric…