Dynamic deconvolution and identification of independent autoregressive sources
研究了观测数少于源数的多变量系统，证明了混合矩阵、AR(1)系数和源分布的可识别性，并提出了简单一致的估计方法，适用于误差变量模型和因果中介模型等。
We consider a multi‐variate system , where the unobserved components are independent AR(1) processes and the number of sources is greater than the number of observed outputs. We show that the mixing matrix , the AR(1) coefficients and distributions of can be identified (up to scale factors of ), 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.