CAJ | 학술논문

本文给出了时间序列中方差的小波系数的两种估计:连续估计和离散估计.这两种估计可以用来检测时间序列中方差的结构变点.利用这两种估计我们给出了方差变点的位置和跳跃幅度的估计,并且显示出这些估计可达到最佳收敛速度.同时,我们还给出了这些估计的收敛速度以及检验统计量的渐进分布!
본문급출료시간서렬중방차적소파계수적량충고계:련속고계화리산고계.저량충고계가이용래검측시간서렬중방차적결구변점.이용저량충고계아문급출료방차변점적위치화도약폭도적고계,병차현시출저사고계가체도최가수렴속도.동시,아문환급출료저사고계적수렴속도이급검험통계량적점진분포!
We propose two estimators, an integral estimator and a discretized estimator, for the wavelet coefficient of volatility in time series models. These estimators can be used to detect the changes of volatility in time series models. The location estimators of the jump points, we proposed, have been shown to have the minimax convergence rate, which is the optimal rate for the estimation of change points. The jump sizes and locations of change points can be consistently estimated by wavelet coefficients. The convergency rates of these estimators are derived and the asymptotic distributions of the statistics are established.