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One of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way. Another challenge is that the number of true change…
Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is…
Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such…
Global climate change is one of main concern of modern society. To estimate this change usually one estimates the global mean temperature. Measuring and calculating the Earth's average temperature are multi-steps complex processes which…
It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that…
The concept of homogeneity plays a critical role in statistics, both in its applications as well as its theory. Change point analysis is a statistical tool that aims to attain homogeneity within time series data. This is accomplished…
Assessing the consistency between short-term global temperature trends in observations and climate model projections is a challenging problem. While climate models capture many processes governing short-term climate fluctuations, they are…
This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…
We analyze the ERA5 reanalysis 2-meter temperature time series on all land grid points using change point analysis. We fit two linear slopes to the data with the constraint that they merge at the point in time where the slope changes. We…
A common approach to detect multiple changepoints is to minimise a measure of data fit plus a penalty that is linear in the number of changepoints. This paper shows that the general finite sample behaviour of such a method can be related to…
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical…
Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…
We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in…
Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points - sudden shifts in the underlying…
This review synthesizes recent advancements in understanding tipping points and cascading transitions within the Earth system, framing them through the lens of nonlinear dynamics and complexity science. It outlines the fundamental concepts…
Linear relations, containing measurement errors in input and output data, are considered. Parameters of these so-called errors-in-variables models can change at some unknown moment. The aim is to test whether such an unknown change has…
Current techniques for predicting climate change are mainly based on "massive" deterministic numerical modeling. However, the ocean-atmosphere system is a so-called "complex system", made up of a large number of interacting elements. We…
Climate change is a non-uniform phenomenon. This paper proposes a new quantitative methodology to characterize, measure, and test the existence of climate change heterogeneity. It consists of three steps. First, we introduce a new testable…
Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…
Time-series forecasting has been an important research domain for so many years. Its applications include ECG predictions, sales forecasting, weather conditions, even COVID-19 spread predictions. These applications have motivated many…