The ACR Model: A Multivariate Dynamic Mixture Autoregression*
提出并分析自回归条件根（ACR）时间序列模型，该多元动态混合自回归模型允许非平稳时期，是阈值自回归或马尔可夫转换模型的替代方案，并证明了其几何遍历性、平稳性及最大似然估计的一致性。
Abstract This paper proposes and analyses the autoregressive conditional root (ACR) time‐series model. This multivariate dynamic mixture autoregression allows for non‐stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis.