Related papers: Sequential change-point detection for generalized …
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $\theta$. We construct the estimator that is…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
A change point detection procedure using the method of moment estimators is proposed. The test statistics is based on a suitable $Z$-process. The asymptotic behavior of this process is established under both the null and the alternative…
For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate…
We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every $\frac{1}{2}<H<1$. More precisely, we extend the consistency proved in \cite{DFW} for $\frac{1}{2}<H<\frac{3}{4}$…
Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the…
We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed…
Ornstein-Uhlenbeck processes driven by general L\'{e}vy process are considered in this paper. We derive strongly consistent estimators for the moments of the underlying L\'{e}vy process and for the mean reverting parameter of the…
A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect…
We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We propose…
One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
The detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems.…
It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…
Time-varying random objects have been increasingly encountered in modern data analysis. Moreover, in a substantial number of these applications, periodic behaviour of the random objects has been observed. We develop a novel procedure to…
There exists a large body of work on online drift detection with the goal of dynamically finding and maintaining changes in data streams. In this paper, we adopt a query-based approach to drift detection. Our approach relies on {\em a drift…
We study multiple change-points detection using multi-samples tests based on U-statistics for absolutely regular observations. Our results extend those of Ngatchou-Wandji et al. (2022) concerned with the study of one single changepoint. The…
This article presents a selective survey of algorithms for the offline detection of multiple change points in multivariate time series. A general yet structuring methodological strategy is adopted to organize this vast body of work. More…
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…