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异方差误差线性模型中多个变点的置信区间AI 解读

We consider the problem of estimating and deriving confidence intervals for change points in linear models with heteroscedastic errors. A CUSUM process-based estimator is proposed, and we establish its asymptotic properties when the linear regression model exhibits change points in both the regression parameters and the distribution of the errors. This theory motivates the construction of confidence sets for multiple change points by refining preliminary change point…

事件时点观测的函数型数据稳定性检验及 IPO 表现应用AI 解读

Many sequentially observed functional data objects are available only at the times of certain events. For example, the trajectory of stock prices of companies after their initial public offering (IPO) can be observed when the offering occurs, and the resulting data may be affected by changing circumstances. It is of interest to investigate whether the mean behavior of such functions is stable over time, and if not, to estimate the times at which apparent changes occur. Since…

高维截面相关面板均值共同断点的检测AI 解读

Summary The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross-sectional dependence is considered. Under the assumption that the cross-sectional dependence is captured by an unknown number of common factors, a new CUSUM-type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross…

一类新的 Rényi 型变点检验统计量AI 解读

A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by Rényi. A thorough asymptotic analysis and simulations both demonstrate that this new class of statistics possess superior power compared to traditional change point statistics based on the CUSUM process when the change point is near the beginning or end of the sample. Generalizations of these “Rényi” statistics are also…

从平稳到轻度非平稳变化的序贯监测AI 解读

We develop and study sequential testing procedures á la Chu et al. (1996) for on-line detection of changes in a time series from stationarity to mild forms of non-stationarity. The proposed tests are based on sequential CUSUM and KPSS-type detector processes, and are shown to provide consistent detection under a wide range of change point models, including changes in the parameters of ARMA and GARCH series from values within the model’s stationarity parameter region to…

Summary Methodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight…

线性面板模型共同变点的 CUSUM 估计量渐近性质AI 解读

We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the cross-sectional units in the form of a common factor. A CUSUM type estimator is proposed, and we establish first and second order asymptotics that can be used to derive consistent confidence intervals for the time of change. Our results improve upon existing theory in two primary directions. Firstly, the conditions we impose on the…

函数型时间序列之间的独立性检验AI 解读

Frequently econometricians are interested in verifying a relationship between two or more time series. Such analysis is typically carried out by causality and/or independence tests which have been well studied when the data is univariate or multivariate. Modern data though is increasingly of a high dimensional or functional nature for which finite dimensional methods are not suitable. In the present paper we develop methodology to check the assumption that data obtained from…

函数型时间序列的平稳性检验AI 解读

Economic and financial data often take the form of a collection of curves observed consecutively over time. Examples include, intraday price curves, yield and term structure curves, and intraday volatility curves. Such curves can be viewed as a time series of functions. A fundamental issue that must be addressed, before an attempt is made to statistically model such data, is whether these curves, perhaps suitably transformed, form a stationary functional time series. This…