论文标题
用于计算非组织时间序列模型对数可能计算梯度和黑森的差分滤波器的强度
An implimentation of the Differential Filter for Computing Gradient and Hessian of the Log-likelihood of Nonstationary Time Series Models
论文作者
论文摘要
状态空间模型和Kalman滤波器为我们提供了统一和计算的有效程序，以计算各种时间序列模型的对数可能性。本文提出了一种用于通过扩展卡尔曼过滤器而无需诉诸数值差异的算法来计算对数可能的梯度和黑森矩阵。与上一篇论文不同（Kitagawa 2020），假定观察噪声方差r = 1。众所周知，对于单变量时间序列，通过最大化该限制模型的对数可能性，我们可以获得与原始状态空间模型相同的估计值。通过这种修改，用于计算梯度和Hessian的算法变得有些复杂。但是，参数矢量的尺寸减少一个，因此在估计状态空间模型的参数方面具有显着优势，尤其是对于相对较低的尺寸参数矢量。提出了三个非组织时间SEIRRES模型的示例，即趋势模型，Statndard季节性调整模型和带有AR组合的季节性调整模型，以举例说明结构矩阵的规范。
The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the gradient and the Hessian matrix of the log-likelihood by extending the Kalman filter without resorting to the numerical difference. Different from the previous paper(Kitagawa 2020), it is assumed that the observation noise variance R=1. It is known that for univariate time series, by maximizing the log-likelihood of this restricted model, we can obtain the same estimates as the ones for the original state-space model. By this modification, the algorithm for computing the gradient and the Hessian becomes somewhat complicated. However, the dimension of the parameter vector is reduce by one and thus has a significant merit in estimating the parameter of the state-space model especially for relatively low dimentional parameter vector. Three examples of nonstationary time seirres models, i.e., trend model, statndard seasonal adjustment model and the seasonal adjustment model with AR componet are presented to exemplified the specification of structural matrices.
