In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (
Shao, 2010
) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (
Baranowski et al., 2019
) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.
Summary
We propose a likelihood ratio scan method for estimating multiple change points in piecewise stationary processes. Using scan statistics reduces the computationally infeasible global multiple‐change‐point estimation problem to a number of single‐change‐point detection problems in various local windows. The computation can be efficiently performed with order O{npt log (n)}. Consistency for the estimated numbers and locations of the change points are established. Moreover, a procedure is developed for constructing confidence intervals for each of the change points. Simulation experiments and real data analysis are conducted to illustrate the efficiency of the likelihood ratio scan method.
Summary
The paper presents a novel non‐linear framework for the construction of flexible multivariate dependence structure (i.e. copulas) from existing copulas based on a straightforward ‘pairwise max‐’rule. The newly constructed max‐copula has a closed form and has strong interpretability. Compared with the classical ‘linear symmetric’ mixture copula, the max‐copula can be viewed as a ‘non‐linear asymmetric’ framework. It is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non‐extremal behaviour modelling. Max‐copulas that are based on single‐factor and block factor models are developed to offer parsimonious modelling for structured dependence, especially in high dimensional applications. Combined with semiparametric time series models, the max‐copula can be used to develop flexible and accurate models for multivariate time series. A new semiparametric composite maximum likelihood method is proposed for parameter estimation, where the consistency and asymptotic normality of estimators are established. The flexibility of the max‐copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments. Real data applications in value‐at‐risk estimation and portfolio optimization for financial risk management demonstrate the max‐copula's promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market.
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
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