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Abstract We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully non-parametric, robust to temporal dependence and avoids the demanding consistent estimation of long-run variance. One salient and distinct feature of the proposed method is its versatility, where it allows change-point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the core of our method, we couple the self-normalisation- (SN) based tests with a novel nested local-window segmentation algorithm, which seems new in the growing literature of change-point analysis. Due to the presence of an inconsistent long-run variance estimator in the SN test, non-standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN-based change-point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state-of-the-art approaches in the literature. 

Abstract We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making. 

Detecting when the underlying distribution changes for the observed time series is a fundamental problem arising in a broad spectrum of applications. In this paper, we study multiple change-point localization in the high-dimensional regression setting, which is particularly challenging as no direct observations of the parameter of interest is available. Specifically, we assume we observe {xt,yt}nt=1 where {xt}nt=1 are p-dimensional covariates, {yt}nt=1 are the univariate responses satisfying 𝔼(yt)=x⊤tβ∗t for 1≤t≤n and {β∗t}nt=1 are the unobserved regression coefficients that change over time in a piecewise constant manner. We propose a novel projection-based algorithm, Variance Projected Wild Binary Segmentation~(VPWBS), which transforms the original (difficult) problem of change-point detection in p-dimensional regression to a simpler problem of change-point detection in mean of a one-dimensional time series. VPWBS is shown to achieve sharp localization rate Op(1/n) up to a log factor, a significant improvement from the best rate Op(1/n‾√) known in the existing literature for multiple change-point localization in high-dimensional regression. Extensive numerical experiments are conducted to demonstrate the robust and favorable performance of VPWBS over two state-of-the-art algorithms, especially when the size of change in the regression coefficients {β∗t}nt=1 is small.