论文标题
Kalman滤波器的梯度和状态空间模型的对数模型的计算计算
Computation of the Gradient and the Hessian of the Log-likelihood of the State-space Model by the Kalman Filter
论文作者
论文摘要
Kalman滤波器可以根据模型的状态空间表示可以获得ARMA模型的最大似然估计。本文提出了一种通过扩展卡尔曼滤波器而不诉诸于数值差的算法来计算对数可能的梯度。列出了季节性调整模型和ARMA模型的三个例子，以说明结构矩阵和初始矩阵的规范。还显示了计算Hessian矩阵的算法的扩展。
The maximum likelihood estimates of an ARMA model can be obtained by the Kalman filter based on the state-space representation of the model. This paper presents an algorithm for computing gradient of the log-likelihood by an extending the Kalman filter without resorting to the numerical difference. Three examples of seasonal adjustment model and ARMA model are presented to exemplified the specification of structural matrices and initial matrices. An extension of the algorithm to compute the Hessian matrix is also shown.
