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Efficient Estimation of the Parameter Path in Unstable Time Series Models

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  • Mueller, Ulrich
  • Petalas, Philippe-Emmanuel

Abstract

The paper investigates asymptotically efficient inference in general likelihood models with time varying parameters. Parameter path estimators and tests of parameter constancy are evaluated by their weighted average risk and weighted average power, respectively. The weight function is proportional to the distribution of a Gaussian process, and focusses on local parameter instabilities that cannot be detected with certainty even in the limit. It is shown that asymptotically, the sample information about the parameter path is efficiently summarized by a Gaussian pseudo model. This approximation leads to computationally convenient formulas for efficient path estimators and test statistics, and unifies the theory of stability testing and parameter path estimation.

Suggested Citation

  • Mueller, Ulrich & Petalas, Philippe-Emmanuel, 2007. "Efficient Estimation of the Parameter Path in Unstable Time Series Models," MPRA Paper 2260, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:2260
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    File URL: https://mpra.ub.uni-muenchen.de/2260/1/MPRA_paper_2260.pdf
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    References listed on IDEAS

    as
    1. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
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    More about this item

    Keywords

    Time Varying Parameters; Non-linear Non-Gaussian Smoothing; Weighted Average Risk; Weighted Average Power; Posterior Approximation; Contiguity;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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