Closed-form expression for finite predictor coefficients of multivariate ARMA processes
Closed-form expression for finite predictor coefficients of multivariate ARMA processes
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多元 ARMA 过程的有限预测系数的封闭式表达式
DOI：
10.1016/j.jmva.2019.104578
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发表时间：
2020
影响因子：
1.6
通讯作者：
Akihiko Inoue
中科院分区：
文献类型：
--
作者：
Makoto Abe;阿部 誠・島 唯史・杉山 俊;Akihiko Inoue
本文导出了多元阿尔马（autoregressive moving-average，ARMA）过程有限预测系数的封闭表达式。该表达式给出的几个显式矩阵是固定的大小独立的观察的数量。该表达式的意义在于，它为我们提供了一种计算有限预测器系数的线性时间算法。在该表达式的证明中，两个相关的矩阵值外函数之间的对应结果起着关键作用。我们应用该表达式来确定自回归模型拟合和自回归筛选自助法中出现的总和的渐进行为。即使对于单变量阿尔马过程，所得结果也是新的。
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes.