Estimation and testing stationarity for double‐autoregressive models
Estimation and testing stationarity for double‐autoregressive models
复制标题
DOI：
10.1111/j.1467-9868.2004.00432.x
复制
发表时间：
2004-02
期刊：
影响因子：
--
通讯作者：
S. Ling
中科院分区：
文献类型：
--
作者：
S. Ling
总结。本文考虑双自回归模型yt=φyt−1+ɛt，其中ɛt=.在Eln|φ+√αηt|1条件下，证明了估计参数的相合性和渐近正态.众所周知，当φt为独立同分布时，这些情形下ɛ的各种估计都不是正态的。我们的结果既新颖又令人惊讶。提出了检验模型平稳性的两个检验方法，并证明了它们的渐近分布是二元布朗运动的函数。文中列出了试验的临界值，并给出了一些模拟结果。给出了美国90天期国库券利率序列的应用。
Summary. The paper considers the double‐autoregressive model yt = φyt−1+ɛt with ɛt =. Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln |φ +√αηt|1 as well as . It is well known that all kinds of estimators of φ in these cases are not normal when ɛt are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for testing stationarity of the model and their asymptotic distributions are shown to be a function of bivariate Brownian motions. Critical values of the tests are tabulated and some simulation results are reported. An application to the US 90‐day treasury bill rate series is given.