滑动平均模型参数估计的Gevers-Wouters算法的指数收敛性

可逆的向量滑动平均(MA)模型参数估计问题本质上是一个矩阵谱分解问题。基于向量MA模型和状态空间模型之间的变换,用Kalman滤波方法证明了矩阵谱分解的Gevers-Wouters算法的一致性和指数收敛性,且证明了收敛速度由MA多项式矩阵的行列式的零点决定。当这些零点不接近单位圆周时,Gevers-Wouters算法可高精度、快速地给出MA参数估计,因而提供一种快速有效的谱分解工具。

Exponential Convergence of Gevers-Wouters Algorithm for Moving Average Model Parameter Estimation

The parameter estimation problem to the invertible vector moving average (MA) model essentially is a matrix spectral factorization problem. By the Kalman filtering method, based on the transformation between the vector MA model and the state space model, the consistence and exponential convergence of the Gevers-Wouters algorithm for matrix spectral factorization is proved, and it is proved that the convergence rate is determined by the zeros of the determinant of the MA polynomial matrix. When these zeros points are not approximate to the unit circle, the Gevers-Wouters algorithm can quickly give the vector MA parameter estimates with the higher accuracy, and provides a fast and efficient spectral factorization tool.