AN INVARIANCE PRINCIPLE FOR SIEVE BOOTSTRAP IN TIME SERIES
证明了筛子自助法在时间序列中的强不变性原理，并验证了该方法在Dickey-Fuller单位根检验中的渐近有效性，为一般线性过程模型使用自助法检验提供了理论依据。
This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form and holds almost surely for all sample realizations. Our development relies upon the strong approximation and the Beveridge–Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickey–Fuller unit root tests for the model driven by a general linear process with independent and identically distributed innovations. We thus provide a theoretical justification on the use of the bootstrap Dickey–Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.