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阈值空间由直线划分的广义多元阈值自回归模型AI 解读

We consider a k-dimensional multiple-regime vector threshold autoregressive model, in which the regime-switching mechanism is governed by a bivariate threshold variable. Specifically, the regimes are induced by a partition of the threshold space by an unknown number of threshold lines. Within each regime, the process follows a specific vector autoregressive (VAR) model. We formulate the model selection and parameter estimation into a minimization problem based on the Minimum…

基于复合似然的时空过程变点检测AI 解读

This article develops a unified and computationally efficient method for change-point estimation along the time dimension in a nonstationary spatio-temporal process. By modeling a nonstationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameter…

时间序列多个变点的自助法推断AI 解读

In this paper, we propose two bootstrap procedures, namely parametric and block bootstrap, to approximate the finite sample distribution of change-point estimators for piecewise stationary time series. The bootstrap procedures are then used to develop a generalized likelihood ratio scan method (GLRSM) for multiple change-point inference in piecewise stationary time series, which estimates the number and locations of change-points and provides a confidence interval for each…

时间序列中变点的最优估计AI 解读

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real…

时间平均协方差矩阵递归估计的自动最优批量选择AI 解读

The time-average covariance matrix (TACM) Σ:=∑k∈ZΓk, where Γk is the auto-covariance function, is an important quantity for the inference of the mean of an Rd-valued stationary process (d ⩾ 1). This article proposes two recursive estimators for Σ with optimal asymptotic mean square error (AMSE) under different strengths of serial dependence. The optimal estimator involves a batch size selection, which requires knowledge of a smoothness parameter ϒβ:=∑k∈Z|k|βΓk, for some β.…

基于分组正交贪婪算法的阈值估计AI 解读

A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection…

利用似然比扫描统计量推断时间序列的多个变点AI 解读

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.…

基于成对似然的多元时间序列变点检测AI 解读

This paper develops a composite likelihood-based approach for multiple changepoint estimation in multivariate time series. We derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment. The number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned…

门限自回归模型的 LASSO 估计AI 解读

This paper develops a novel approach for estimating a threshold autoregressive (TAR) model with multiple-regimes and establishes its large sample properties. By reframing the problem in a regression variable selection context, a least absolute shrinkage and selection operator (LASSO) procedure is proposed to estimate a TAR model with an unknown number of thresholds, where the computation can be performed efficiently. It is further shown that the number and the location of…

含结构突变的多区制门限自回归模型估计AI 解读

The threshold autoregressive (TAR) model is a class of nonlinear time series models that have been widely used in many areas. Due to its nonlinear nature, one major difficulty in fitting a TAR model is the estimation of the thresholds. As a first contribution, this article develops an automatic procedure to estimate the number and values of the thresholds, as well as the corresponding AR order and parameter values in each regime. These parameter estimates are defined as the…

结构突变时间序列的组 LASSOAI 解读

Consider a structural break autoregressive (SBAR) process where j = 1, …, m + 1, {t1, …, tm} are change-points, 1 = t0 < t1 < ⋅⋅⋅ < tm + 1 = n + 1, σ( · ) is a measurable function on , and {ϵt} are white noise with unit variance. In practice, the number of change-points m is usually assumed to be known and small, because a large m would involve a huge amount of computational burden for parameters estimation. By reformulating the problem in a variable selection context, the…