MAXIMUM LIKELIHOOD IDENTIFICATION OF GAUSSIAN AUTOREGRESSIVE MOVING AVERAGE MODELS
MAXIMUM LIKELIHOOD IDENTIFICATION OF GAUSSIAN AUTOREGRESSIVE MOVING AVERAGE MODELS
复制标题
DOI：
10.1093/biomet/60.2.255
复制
发表时间：
1973-01-01
期刊：
影响因子：
2.7
通讯作者：
AKAIKE, H
中科院分区：
文献类型：
--
作者：
AKAIKE, H
摘要给出了多维自回归滑动平均高斯过程对数似然函数的渐近逼近的梯度封闭形式表示和Hessian近似。讨论了它们用于似然函数的数值最大化。本文证明了Hannan（1969）描述的一维自回归滑动平均过程参数估计的过程等价于利用梯度和近似Hessian函数求似然函数数值最大值的Newton-Raphson过程的一步的三阶段实现。这使得将该过程扩展到多维情况变得简单。利用块Toeplitz型特性的近似Hessian指出。
SUMMARYClosed form representations of the gradients and an approximation to the Hessian are given for an asymptotic approximation to the log likelihood function of a multidimensional autoregressive moving average Gaussian process. Their use for the numerical maximization of the likelihood function is discussed. It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a three-stage realization of one step of the Newton-Raphson procedure for the numerical maximization of the likelihood function, using the gradient and the approximate Hessian. This makes it straightforward to extend the procedure to the multidimensional case. The use of the block Toeplitz type characteristic of the approximate Hessian is pointed out.