Nonasymptotic bounds for autoregressive time series modeling
自回归时间序列建模的非渐近界
The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR($\infty$) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finiteorder AR model. A lower bound on the accuracy of AR approximations is derived, and a nonasymptotic upper bound on…