Econ Papers Daily / 期刊论文
自回归运动定律的通解
The general solution to an autoregressive law of motion
摘要
We provide a complete description of the set of all solutions to a vector autoregressive law of motion. Every solution is shown to be the sum of three components, each corresponding to a directed flow of time. One component flows forward from the arbitrarily distant past, one flows backward from the arbitrarily distant future, and one flows outward from time zero. The three components are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive coefficient matrix according to whether they are inside, outside, or on the unit circle. We establish a one‐to‐one correspondence between the set of all solutions and a finite‐dimensional space of initial conditions.
中文摘要
我们完整描述了向量自回归运动方程所有解集的构成。每个解均可分解为三个分量之和，分别对应三种时间流向：一个分量从任意遥远的过去向前流动，一个分量从任意遥远的未来向后流动，一个分量从零时刻向外扩散。这三个分量通过将三种互补谱投影算子作用于解而获得，其对应自回归系数矩阵特征值按单位圆内、外及圆上的分类。我们建立了所有解集与有限维初始条件空间之间的一一对应关系。