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Exploiting infinite variance through Dummy Variables in non-stationary autoregressions

Author

Listed:
  • 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.

Suggested Citation

  • Giuseppe Cavaliere & Iliyan Georgiev, 2013. "Exploiting infinite variance through Dummy Variables in non-stationary autoregressions," Quaderni di Dipartimento 1, Department of Statistics, University of Bologna.
    • Handle: RePEc:bot:quadip:wpaper:118
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    References listed on IDEAS

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    6. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," Discussion Papers 11-29, University of Copenhagen. Department of Economics.
    7. Cavaliere, Giuseppe & Georgiev, Iliyan, 2009. "Robust Inference In Autoregressions With Multiple Outliers," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1625-1661, December.
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    10. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
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    12. Bent Nielsen & Soren Johansen, 2010. "Discussion of The Forward Search: Theory and Data Analysis," Economics Series Working Papers 2010-W02, University of Oxford, Department of Economics.
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    Cited by:

    1. Søren Johansen & Bent Nielsen, 2011. "Asymptotic theory for iterated one-step Huber-skip estimators," Discussion Papers 11-29, University of Copenhagen. Department of Economics.
    2. Søren Johansen & Lukasz Gatarek, 2014. "Optimal hedging with the cointegrated vector autoregressive model," CREATES Research Papers 2014-40, Department of Economics and Business Economics, Aarhus University.
    3. Bent Nielsen & Xiyu Jiao, 2016. "Asymptotic Analysis of Iterated 1-step Huber-skip M-estimators with Varying Cut-offs," Economics Papers 2016-W08, Economics Group, Nuffield College, University of Oxford.
    4. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    5. Katleho Makatjane, 2022. "Forecasting Uncertainty Intervals for Return Period of Extreme Daily Electricity Consumption," International Journal of Energy Economics and Policy, Econjournals, vol. 12(4), pages 217-225, July.
    6. Søren Johansen & Bent Nielsen, 2013. "Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator," Econometrics, MDPI, vol. 1(1), pages 1-18, May.

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