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Exploiting infinite variance through Dummy Variables in non-stationary autoregressions

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Author Info

  • Giuseppe Cavaliere

    ()
    (Università di Bologna)

  • Iliyan Georgiev

    (Universidade Nova de Lisboa)

Abstract

We consider estimation and testing infinite-order autoregressive models with a (near) unit root and infinite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out ?large?innovations, i.e., exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold which ensure that (i) the dummy-based estimator is consistent at higher rates than the OLS estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

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Bibliographic Info

Paper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 1.

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Length: 31
Date of creation: 2013
Date of revision:
Handle: RePEc:bot:quadip:118

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Keywords: Autoregressive processes; Infinite variance; Dummy variables Processi autoregressivi; Varianza infinita; Variabili dumm;

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References

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  1. Cavaliere, Giuseppe & Georgiev, Iliyan, 2009. "Robust Inference In Autoregressions With Multiple Outliers," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1625-1661, December.
  2. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
  3. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, 07.
  4. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," Discussion Papers 11-29, University of Copenhagen. Department of Economics.
  5. Resnick, Sidney & Greenwood, Priscilla, 1979. "A bivariate stable characterization and domains of attraction," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 206-221, June.
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Cited by:
  1. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," CREATES Research Papers 2011-40, School of Economics and Management, University of Aarhus.
  2. Søren Johansen & Bent Nielsen, 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 53-70, May.

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