ESTIMATING LINEAR DYNAMICAL SYSTEMS USING SUBSPACE METHODS
利用子空间方法估计线性动态系统AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究 ARMAX、ARMA 与 I(1) 动态系统的估计及阶数选择，属于时间序列方法。
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利用子空间方法估计线性动态系统
- 研究问题
- 基于回归的子空间方法如何估计 ARMAX 动态系统，在平稳与一阶单整情形下具有哪些统计性质，设计参数如何自动选择？
- 方法与思路
- 作者综述以 CCA 为代表的子空间方法，汇总正确设定下的渐近结果，并讨论系统阶数等设计参数对估计和自动化的影响。
- 材料陈述的贡献
- 摘要称，这些方法在所述条件下可获一致性和渐近正态性；特定高斯 ARMA 情形下渐近有效，且提供模型复杂度评估信息与自动选择建议。
- 阅读关注点
- 应核对条件异方差和外生输入的要求、平稳与 I(1) 结果的区别，以及系统阶数等设计参数的自动选择是否保留理论性质。
- 阅读边界
- 仅依据所给 Crossref 摘要；结果以正确设定等条件为前提，渐近有效性限定于独立同分布高斯创新的平稳 ARMA，亦不推断版本变化。
原文摘要
This paper provides a survey on a class of so-called subspace methods whose main proponent is CCA proposed by Larimore (1983, Proceedings of the 1983 American Control Conference 2 ). Because they are based on regressions these methods for the estimation of ARMAX systems are attractive as a result of their conceptual simplicity and their numerical advantages as compared to traditional estimators based on criterion optimization. Under the assumption of correct specification the methods provide consistent and asymptotically normal estimates for stationary ARMAX processes where the innovations may be conditionally heteroskedastic and the exogenous inputs are strictly stationary of sufficiently short memory. For stationary autoregressive moving average (ARMA) processes with independent and identically distributed (i.i.d.) Gaussian innovations the estimates are even asymptotically efficient. For I (1) ARMA processes the estimates of both the long-run and the short-run dynamics are consistent without using the knowledge that the data are integrated in the algorithm. Additionally the algorithms provide easily accessible information on the appropriateness of the chosen model complexity. The algorithms include a number of design parameters that have to be set by the user. These include the order of the estimated system. This paper collects up-to-date knowledge on the effects of these design parameters, leading to a number of suggested automated choices to obtain a fully automated estimation procedure.