论文标题
非线性矢量自回归过程的独立创新分析
Independent Innovation Analysis for Nonlinear Vector Autoregressive Process
论文作者
论文摘要
非线性矢量自回旋（NVAR）模型提供了一个吸引人的框架，以分析从非线性动力学系统获得的多元时间序列。但是，通过驱动动力学来起着关键作用的创新（或错误）几乎总是被认为是加性的。添加性极大地限制了模型的一般性，阻碍了对创新之间具有非线性相互作用的一般NVAR过程的分析。在这里，我们提出了一个称为独立创新分析（IIA）的新的通用框架，该框架估计了完全NVAR的创新。我们假设创新的相互独立性及其通过辅助变量的调制（通常被视为时间索引，并简单地被解释为非组织性）。我们表明，IIA可以保证具有任意非线性创新的可识别性，直到置换和组成部分可逆性的非线性。我们还根据辅助变量的类型提出了三个估计框架。因此，我们为NVAR将军提供了第一个严格的可识别性结果，以及学习此类模型的非常通用的工具。
The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the dynamics, is almost always assumed to be additive. Additivity greatly limits the generality of the model, hindering analysis of general NVAR processes which have nonlinear interactions between the innovations. Here, we propose a new general framework called independent innovation analysis (IIA), which estimates the innovations from completely general NVAR. We assume mutual independence of the innovations as well as their modulation by an auxiliary variable (which is often taken as the time index and simply interpreted as nonstationarity). We show that IIA guarantees the identifiability of the innovations with arbitrary nonlinearities, up to a permutation and component-wise invertible nonlinearities. We also propose three estimation frameworks depending on the type of the auxiliary variable. We thus provide the first rigorous identifiability result for general NVAR, as well as very general tools for learning such models.
