Predictability, real time estimation, and the formulation of unobserved components models
研究了不可观测成分模型在设定时因扰动项时序和协方差矩阵不同导致的观测等价问题，发现点预测和实时估计不受协方差设定影响，但可靠性仅在特殊情况下可识别。
The formulation of unobserved components models raises some relevant interpretative issues, owing to the existence of alternative observationally equivalent specifications, differing for the timing of the disturbances and their covariance matrix. We illustrate them with reference to unobserved components models with ARMA(m, m) reduced form, performing the decomposition of the series into an ARMA(m, q) signal, q≤m, and a noise component. We provide a characterization of the set of covariance structures that are observationally equivalent, when the models are formulated both in the future and the contemporaneous forms. Hence, we show that, while the point predictions and the contemporaneous real time estimates are invariant to the specification of the disturbances covariance matrix, the reliability cannot be identified, except for special cases requiring q<m−1.