We consider a multi-variate system $\text{◂=▸}{Y}_t=A{X}_t$, where the unobserved components $X_t$ are independent AR(1) processes and the number of sources is greater than the number of observed outputs. We show that the mixing matrix $A$, the AR(1) coefficients and distributions of $X_t$ can be identified (up to scale factors of $X_t$), which solves the dynamic deconvolution problem. The proof is constructive and allows us to introduce simple consistent estimators of all unknown scalar and functional parameters of the model. The approach is illustrated by an estimation and identification of the dynamics of unobserved short- and long-run components in a time series. Applications to causal models with structural innovations are also discussed, such as the identification in error-in-variables models and causal mediation models.

中文翻译：

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独立自回归源的动态反卷积和识别

我们考虑一个多变量系统$\text{◂=▸}{是}_{吨}=A{X}_{吨}$，其中未观察到的组件$X_{吨}$是独立的 AR(1) 过程，源的数量大于观察到的输出的数量。我们证明混合矩阵$A$, 的 AR(1) 系数和分布$X_{吨}$可以识别（高达比例因子$X_{吨}$)，它解决了动态反卷积问题。该证明是建设性的，允许我们引入模型所有未知标量和函数参数的简单一致估计量。通过估计和识别时间序列中未观察到的短期和长期组件的动态来说明该方法。还讨论了具有结构创新的因果模型的应用，例如变量模型和因果中介模型中的错误识别。