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Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions

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  • Cavaliere, Giuseppe
  • Georgiev, Iliyan

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

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 29 (2013)
Issue (Month): 06 (December)
Pages: 1162-1195

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Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1162-1195_00

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  1. 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.
  2. Bent Nielsen & Eric Engler, 2007. "The empirical process of autoregressive residuals," Economics Papers 2007-W01, Economics Group, Nuffield College, University of Oxford.
  3. Cavaliere, Giuseppe & Georgiev, Iliyan, 2009. "Robust Inference In Autoregressions With Multiple Outliers," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1625-1661, December.
  4. 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.
  5. 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.
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Cited by:
  1. 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.
  2. 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.

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