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伪结构断点现象札记AI 解读

When the disturbances of a regression model follow an I (1) process there is a tendency to estimate a break point in the middle of the sample, even though a break point does not actually exist. In this note, we provide a mathematical proof for this phenomenon.

This paper develops methods for constructing asymptotically valid confidence intervals for the date of a single break in multivariate time series, including I(0), I(1), and deterministically trending regressors. Although the width of the asymptotic confidence interval does not decrease as the sample size increases, it is inversely related to the number of series which have a common break date, so there are substantial gains to multivariate inference about break dates. These…

含多重结构变化的线性模型：估计与检验AI 解读

This paper develops the statistical theory for testing and estimating multiple change points in regression models. The rate of convergence and limiting distribution for the estimated parameters are obtained. Several test statistics are proposed to determine the existence as well as the number of change points. A partial structural change model is considered. The authors study both fixed and shrinking magnitudes of shifts. In addition, the models allow for serially correlated…

逐一估计多个结构断点AI 解读

Sequential (one-by-one) rather than simultaneous estimation of multiple breaks is investigated in this paper. The advantage of this method lies in its computational savings and its robustness to misspecification in the number of breaks. The number of least-squares regressions required to compute all of the break points is of order T , the sample size. Each estimated break point is shown to be consistent for one of the true ones despite underspecification of the number of…

线性回归中的参数恒定性检验：经验分布函数方法AI 解读

This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free. The proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending…

线性回归中突变的最小绝对偏差估计AI 解读

This paper develops the asymptotic theory for least absolute deviation estimation of a shift in linear regressions. Rates of convergence and asymptotic distributions for the estimated regression parameters and the estimated shift point are derived. The asymptotic theory is developed both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases. Asymptotic distributions are also obtained for trending regressors and for…

ARMA模型残差序贯经验过程的弱收敛AI 解读

This paper studies the weak convergence of the sequential empirical process $\widehat{K}_n$ of the estimated residuals in ARMA$(p, q)$ models when the errors are independent and identically distributed. It is shown that, under some mild conditions, $\widehat{K}_n$ converges weakly to a Kiefer process. The weak convergence is discussed for both finite and infinite variance time series models. An application to a change-point problem is considered.