Properties of the nonparametric autoregressive bootstrap
研究了非参数自回归模型的自回归自助法，证明其能正确逼近自回归函数的置信带以及参数统计量的分布，适用于时间序列分析。
For nonparametric autoregression, we investigate a model based bootstrap procedure (`autoregressive bootstrap') that mimics the complete dependence structure of the original time series. We give consistency results for uniform bootstrap confidence bands of the autoregression function based on kernel estimates of the autoregression function. This result is achieved by global strong approximations of the kernel estimates for the resample and for the original sample. Furthermore, it is obtained that the autoregressive bootstrap also yields asymptotically correct approximations for distributions of parametric statistics, for which regression‐type bootstrap‐techniques like the wild bootstrap do not work. For this purpose, we prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. We propose some particular estimators of the autoregression function and of the density of the innovations such that the mixing coefficients of the autoregressive bootstrap process can be bounded uniformly by some exponentially decaying sequence. This is achieved by using well‐established coupling techniques. Moreover, by using some `decoupling' argument, we show that the stationary density of the bootstrap process converges to that of the original process. The paper may serve as a template for proving similar consistency results for other bootstrap techniques such as the Markov bootstrap.