论文标题
在一系列几乎不稳定的过程中的一致性和渐近正态性
Consistency and asymptotic normality in a class of nearly unstable processes
论文作者
论文摘要
本文涉及一类稳定但几乎不稳定的过程的推论。考虑了自回旋过程，其中稳定性和不稳定性之间的桥梁由随时间变化的伴侣矩阵$ a_ {n} $带有频谱半径$ρ（a_ {n}）<1 $满足$ρ（a_ {n}）<rightarrow 1 $。该框架特别适合通过关注单元圆的内部边界来理解单位根问题。在经验协方差和OLS估计中建立了一致性，以及在适当的假设下$ a $，$ a_n $的限制时具有渐近正态性，具有真实的频谱，并且当$ a $ a $ conter contry contry contres conpection complect eigenvalues时会推荐特定的案例。渐近过程与一个单位根（位于1或$ -1 $），甚至两个位于1和$ -1 $的单位根集成。最后，一组模拟说明了OLS的渐近行为。结果基本上通过$ l^2 $计算证明了Martingales的三角形阵列的极限理论。
This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $ρ(A_{n}) < 1$ satisfying $ρ(A_{n}) \rightarrow 1$. This framework is particularly suitable to understand unit root issues by focusing on the inner boundary of the unit circle. Consistency is established for the empirical covariance and the OLS estimation together with asymptotic normality under appropriate hypotheses when $A$, the limit of $A_n$, has a real spectrum, and a particular case is deduced when $A$ also contains complex eigenvalues. The asymptotic process is integrated with either one unit root (located at 1 or $-1$), or even two unit roots located at 1 and $-1$. Finally, a set of simulations illustrate the asymptotic behavior of the OLS. The results are essentially proved by $L^2$ computations and the limit theory of triangular arrays of martingales.
