SUBGEOMETRICALLY ERGODIC AUTOREGRESSIONS
研究了如何利用马尔可夫链理论中的次几何遍历性来分析非线性时间序列模型的平稳性和遍历性，将一阶结果推广到高阶情形，并证明了在适当条件下模型具有次几何遍历性及相应的β混合性。
In this paper, we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications, we also obtain stationarity and $\beta $ -mixing with subgeometrically decaying mixing coefficients.