Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models
提出一种新的精确解析解，用于初始化具有扩散初始条件的状态空间模型的卡尔曼滤波，适用于含随机趋势、季节成分等非平稳成分的回归模型，计算高效且易于实现。
This article presents a new exact solution for the initialization of the Kalman filter for state space models with diffuse initial conditions. For example, the regression model with stochastic trend, seasonal and other nonstationary autoregressive integrated moving average components requires a (partially) diffuse initial state vector. The proposed analytical solution is easy to implement and computationally efficient. The exact solution for smoothing is also given. Missing observations are handled in a straightforward manner. All proofs rely on elementary results.