Related papers: Segmentation algorithm for non-stationary compound…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a…

In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use…

In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary…

We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally…

Segmented models are widely used to describe non-stationary sequential data with discrete change points. Their estimation usually requires solving a mixed discrete-continuous optimization problem, where the segmentation is the discrete part…

The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…

In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…

A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…

To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach…

Although the applications of Non-Homogeneous Poisson Processes to model and study the threshold overshoots of interest in different time series of measurements have proven to provide good results, they needed to be complemented with an…

We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…

The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…

Modern time series data often exhibit complex dependence and structural changes which are not easily characterised by shifts in the mean or model parameters. We propose a nonparametric data segmentation methodology for multivariate time…

While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current…

Due to the increasing complexity and interconnectedness of different components in modern automotive software systems there is a great number of interactions between these system components and their environment. These interactions result…