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On the Estimation of Nonlinearly Aggregated Mixed Models

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Author Info
Tommaso Proietti (Dipartimento di Scienze Statistiche, Udine)

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Abstract

The article proposes an iterative algorithm for the estimation of fixed and random effects of a nonlinearly aggregated mixed model. The latter arises when an additive Gaussian model is formulated at the disaggregate level on a nonlinear transformation of the responses, but information is available in aggregate form. The nonlinear transformation breaks the linearity of the aggregate model, yielding a nonlinear tight observational constraint. The algorithm rests upon the sequential linearization of the nonlinear aggregation constraint around proposals that are iteratively updated until convergence. Likelihood inferences on the hyperparameters are also discussed. As a by product we provide a solution to the problem of disaggregating over the units of analysis the aggregate responses, enforcing the nonlinear observational constraints. Illustrations are provided with reference to the temporal disaggregation problem, concerning the distribution of annual time series flows to the quarters making up the year.

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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 0411012.

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Length: 19 pages
Date of creation: 15 Nov 2004
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Handle: RePEc:wpa:wuwpem:0411012

Note: Type of Document - pdf; pages: 19
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Web page: http://129.3.20.41

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Related research
Keywords: Temporal and spatial disaggregation; Best linear unbiased prediction; Box-Cox transformation; Constrained nonlinear optimization.;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-75, November. [Downloadable!] (restricted)
  2. Robert B. Litterman, 1983. "A random walk, Markov model for the distribution of time series," Staff Report 84, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  3. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  4. Fernandez, Roque B, 1981. "A Methodological Note on the Estimation of Time Series," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 471-76, August. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Proietti, Tommaso, 2008. "Structural Time Series Models for Business Cycle Analysis," MPRA Paper 6854, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  2. Andrea, SILVESTRINI, 2005. "Temporal aggregaton of univariate linear time series models," Discussion Papers (ECON - Département des Sciences Economiques) 2005044, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
    Other versions:
  3. Tommaso Proietti, 2004. "Temporal Disaggregation by State Space Methods: Dynamic Regression Methods Revisited," Econometrics 0411011, EconWPA. [Downloadable!]
    Other versions:
  4. Frale, Cecilia & Marcellino, Massimiliano & Mazzi, Gian Luigi & Proietti, Tommaso, 2008. "A Monthly Indicator of the Euro Area GDP," CEPR Discussion Papers 7007, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  5. Cecilia Frale & David Veredas, 2008. "A Monthly Volatility Index for the US Economy," ECARES Working Papers 2008_008, Université Libre de Bruxelles, Ecares. [Downloadable!]
  6. Andrea Silvestrini & David Veredas, 2008. "Temporal aggregation of univariate and multivariate time series models: A survey," Temi di discussione (Economic working papers) 685, Bank of Italy, Economic Research Department. [Downloadable!]
    Other versions:
  7. Proietti, Tommaso, 2008. "Estimation of Common Factors under Cross-Sectional and Temporal Aggregation Constraints: Nowcasting Monthly GDP and its Main Components," MPRA Paper 6860, University Library of Munich, Germany. [Downloadable!]
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