Predictability, Real Time Estimation, and the Formulation of Unobserved Components Models

Proietti Tommaso
CEIS Research Paper
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.

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Number: 455
Keywords: ARMA models,Steady State Kalman filter,Correlated Components,Nonfundamentalness
JEL codes: C22, C51, C53.
Volume: 17
Issue: 3
Date: Friday, March 22, 2019
Revision Date: Friday, March 22, 2019