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Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…

Statistics Theory · Mathematics 2016-07-19 Stefan Birr , Stanislav Volgushev , Tobias Kley , Holger Dette , Marc Hallin

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…

Probability · Mathematics 2017-07-27 Andrea Granelli , Almut E. D. Veraart

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…

Applications · Statistics 2014-06-02 Daniele Durante , Bruno Scarpa , David B. Dunson

In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the explanatory variables number is large. We build…

Methodology · Statistics 2020-07-31 Gabriela Ciuperca

Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional…

Methodology · Statistics 2026-05-28 Serhii Zabolotnii

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…

Statistics Theory · Mathematics 2023-02-28 Yunyi Zhang , Efstathios Paparoditis , Dimitris N. Politis

Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…

Statistics Theory · Mathematics 2025-09-12 Yunyi Zhang

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…

Machine Learning · Computer Science 2016-06-23 Nathanael Perraudin , Andreas Loukas , Francesco Grassi , Pierre Vandergheynst

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…

Statistics Theory · Mathematics 2017-04-11 Hossein Keshavarz , Clayton Scott , XuanLong Nguyen

An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…

Statistics Theory · Mathematics 2016-07-19 Philip Preuß , Kemal Sen , Holger Dette

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Machine Learning · Computer Science 2015-06-11 Arash Amini , Ulugbek S. Kamilov , Emrah Bostan , Michael Unser

In this paper easily applicable techniques are devised for detecting changepoints in autocorrelated Gaussian sequences. Our method proceeds by sequential evaluation of a CUSUM-type test statistic, which is compared to a predefined…

Probability · Mathematics 2016-02-09 W. Ellens , J. Kuhn , M. Mandjes , P. Żuraniewski

We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…

Statistics Theory · Mathematics 2020-10-01 Annika Betken , Martin Wendler

In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…

Probability · Mathematics 2014-02-07 José Manuel Corcuera , David Nualart , Mark Podolskij

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…

Methodology · Statistics 2021-10-25 Tomas Masak , Victor M. Panaretos

We show optimality, in a well-defined sense, using cumulative sum (CUSUM) charts for detecting changes in distributions. We consider a setting with multiple changes between two known distributions. This result advocates the use of…

Methodology · Statistics 2012-05-10 F. Din-Houn Lau , Axel Gandy

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…

Statistics Theory · Mathematics 2021-05-24 Sara Kristin Schmidt , Max Wornowizki , Roland Fried , Herold Dehling

In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic…

Methodology · Statistics 2023-04-17 Degui Li , Runze Li , Han Lin Shang

Traditional normalization techniques (e.g., Batch Normalization and Instance Normalization) generally and simplistically assume that training and test data follow the same distribution. As distribution shifts are inevitable in real-world…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Zhiqiang Tang , Yunhe Gao , Yi Zhu , Zhi Zhang , Mu Li , Dimitris Metaxas

One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…

Statistics Theory · Mathematics 2024-12-20 Fabian Mies