Functional Estimation and Change Detection for Nonstationary Time Series
针对非平稳时间序列，构建了局部平稳过程积分参数的估计量，并建立泛函中心极限定理，实现对峰度、自相关等参数的结构断点检验，通过自助法进行可行推断，并应用于高频资产价格。
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this article, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad class of parameters under mild assumptions. The proposed framework covers all parameters which may be expressed as nonlinear functions of moments, for example kurtosis, autocorrelation, and coefficients in a linear regression model. To perform feasible inference based on the derived limit distribution, a bootstrap variant is proposed and its consistency is established. The methodology is illustrated by means of a simulation study and by an application to high-frequency asset prices.