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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. 

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.

 

We introduce an L2-type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed on the basis of the pairwise distance covariance and it accounts for the non-linear and non-monotone dependences among the data, which cannot be fully captured by the existing tests based on either Pearson correlation or rank correlation. Our test can be conveniently implemented in practice as the limiting null distribution of the test statistic is shown to be standard normal. It exhibits excellent finite sample performance in our simulation studies even when the sample size is small albeit the dimension is high and is shown to identify non-linear dependence in empirical data analysis successfully. On the theory side, asymptotic normality of our test statistic is shown under quite mild moment assumptions and with little restriction on the growth rate of the dimension as a function of sample size. As a demonstration of good power properties for our distance-covariance-based test, we further show that an infeasible version of our test statistic has the rate optimality in the class of Gaussian distributions with equal correlation.

 

The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide a more accurate approximation to the finite sample distribution than the conventional χ2-approximation. Our theoretical and numerical findings suggest that both the finite sample and the large sample upper bounds for coverage probabilities are strictly less than 1 and the blockwise empirical likelihood confidence region can exhibit serious undercoverage when the dimension of moment conditions is moderate or large, the time series dependence is positively strong or the block size is large relative to the sample size. A similar finite sample coverage problem occurs for non-standard expansive empirical likelihood. To alleviate the coverage bound problem, we propose to penalize both empirical likelihood methods by relaxing the convex hull constraint. Numerical simulations and data illustrations demonstrate the effectiveness of our proposed remedies in terms of delivering confidence sets with more accurate coverage. Some technical details and additional simulation results are included in on-line supplemental material.