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英文文献：Unit Root Vector Autoregression with volatility Induced Stationarity-具有波动率引起平稳性的单位根向量自回归
英文文献作者：Anders Rahbek,Heino Bohn Nielsen
英文文献摘要：
We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time maintain stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have no finite first-order moments, but remain strictly stationary and ergodic, while they co-move in the sense that their spread has no unit root. The model thus allows for volatility induced stationarity, and the paper shows conditions under which the multivariate process is strictly stationary and geometrically ergodic. Interestingly, these conditions include the case of unit roots and a reduced rank structure in the conditional mean, known from linear co-integration to imply non-stationarity. Asymptotic theory of the maximum likelihood estimators for a particular structured case (so-called self-exciting) is provided, and it is shown that square-root T convergence to Gaussian distributions apply despite unit roots as well as absence of finite first and higher order moments. Monte Carlo simulations confirm the usefulness of the asymptotics in finite samples.
我们提出了一个离散时间多元模型，其中滞后水平的过程进入条件均值和条件方差。这样，我们就可以在经验上观察到时间序列(如利率)的持续性，这通常意味着单位根，但同时，尽管有这样的单位根，我们仍然保持平稳性。具体来说，该模型连接了向量自回归和用滞后水平替换残差的多元ARCH模型。利用最近的美国期限结构数据给出了一个经验的例证，其中个别利率有单位根，没有有限的一阶矩，但保持严格平稳和遍历，而他们的共同移动的意义上，他们的利差没有单位根。因此，该模型允许波动引起的平稳性，并给出了多元过程是严格平稳和几何遍历的条件。有趣的是，这些条件包括单位根和条件均值中秩结构的减少，从线性协整可知，表示非平稳性。摘要给出了一种特殊结构情形(所谓自激)的极大似然估计的渐近理论，并证明了在没有单位根和有限一阶及高阶矩的情况下，平方根T收敛于高斯分布。蒙特卡洛模拟验证了该渐近在有限样本中的有效性。
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