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

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Abstract

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

Suggested Citation

  • Tommaso Proietti, 2019. "Predictability, Real Time Estimation, and the Formulation of Unobserved Components Models," CEIS Research Paper 455, Tor Vergata University, CEIS, revised 22 Mar 2019.
  • Handle: RePEc:rtv:ceisrp:455
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    Keywords

    ARMA models; Steady State Kalman filter; Correlated Components; Nonfundamentalness;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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