ON THE IDENTIFICATION AND ESTIMATION OF NONSTATIONARY AND COINTEGRATED ARMAX SYSTEMS
非平稳与协整 ARMAX 系统的识别和估计AI 解读 ↓
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非平稳与协整 ARMAX 系统的识别和估计
- 研究问题
- 如何将向量动态系统的识别和估计理论扩展到给定初始条件的非平稳与协整 ARMAX 过程，并构造可计算的似然？
- 方法与思路
- 作者结合随机差分方程与调整后的 Kronecker 指数理论，推导阶梯规范形和误差修正表示，并给出新息似然算法。
- 材料陈述的贡献
- 摘要称，论文给出协整系统的识别条件、精确高斯似然算法，以及近似高斯估计和精确极大似然估计的渐近性质。
- 阅读关注点
- 应核对阶梯规范形的参数约束、初始条件处理、协整秩与识别条件，以及两种估计量的分布和算法实现。
- 阅读边界
- 仅据 RePEc 所载出版社摘要；摘要未列明识别条件、极限分布或实验数值，不能判断高斯似然结论在非高斯误差下的范围。
原文摘要
This paper extends current theory on the identification and estimation of vector time series models to nonstationary processes. It examines the structure of dynamic simultaneous equations systems or ARMAX processes that start from a given set of initial conditions and evolve over a given, possibly infinite, future time horizon. The analysis proceeds by deriving the echelon canonical form for such processes. The results are obtained by amalgamating ideas from the theory of stochastic difference equations with adaptations of the Kronecker index theory of dynamic systems. An extension of these results to the analysis of unit-root, partially nonstationary (cointegrated) time series models is also presented, leading to straightforward identification conditions for the error correction, echelon canonical form. An innovations algorithm for the evaluation of the exact Gaussian likelihood is given. The asymptotic properties of the approximate Gaussian estimator and the exact maximum likelihood estimator based upon the algorithm are derived for the cointegrated case. Examples illustrating the theory are discussed, and some experimental evidence is also presented.I thank two referees for insightful comments and helpful suggestions on the content and presentation of this paper. I am particularly grateful for the correction of errors in earlier drafts and reference to the work of B. Hanzon. Financial support under ARC grant DP0343811 is gratefully acknowledged.