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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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  • Cavaliere, Giuseppe & Georgiev, Iliyan, 2013. "Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1162-1195, December.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1162-1195_00
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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, April.
    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.
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    Cited by:

    1. 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.
    2. 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.
    3. Lukasz Gatarek & Søren Johansen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-22, University of Copenhagen. Department of Economics.

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