基于稀疏组Lasso的分段平稳自回归模型变点检测方法

Change point detecting of piecewise stationary auto regressive model based on sparse group Lasso

结构变化检测是分析系统动态规律的重要方式之一.针对分段平稳自回归模型,将变点检测问题转化为变量选择问题,采用稀疏组Lasso方法得到变点个数和位置的初始估计,提出分组选择方法在初始估计的变点中进行选择,然后用后向删除法得到变点个数及位置的估计.证明了提出的方法对变点个数和位置估计的一致性.另外,稀疏组Lasso方法通过约束变点位置上模型参数的稀疏性,能够进一步确定回归系数发生变化的具体滞后变量阶数.最后,仿真实验和应用实例证实,相对于直接应用后向删除法,分组选择方法的引入显著提高了估计的效率;相对于组Lasso方法,稀疏组Lasso方法可以进一步识别在变点位置上发生变化的具体滞后变量阶数.

Structural change detection is one of the important ways to analyze the dynamical law of systems.For the piecewise stationary autoregressive model,this paper transforms the change point detection problem into a variable selection problem.The sparse group Lasso method is used to obtain the initial estimation of the number and location of change points.A group selection method is proposed to select the change points in the initial estimation.Then,the number and locations of the change points are estimated by the backward elimination algorithm.The consistency of the proposed method for the number and locations estimation of change points is proved.In addition,by constraining the sparsity of model parameters at the position of change points,the sparse group Lasso method can further determine the specific lag variable order where the regressive coefficients change.Finally,simulation experiments and application examples illustrate that the introduction of group selection method significantly improves the estimation efficiency than the direct application of backward deletion method and that the sparse group lasso method can further identify the specific order of lag variables which change at the change point.