时间序列中方差的结构变点的小波识别(英文)

Wavelet Identification of Structural Change Points in Volatility Models for Time Series

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!

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.