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EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS

Published online by Cambridge University Press:  13 August 2013

Giuseppe Cavaliere and
Iliyan Georgiev
Giuseppe Cavaliere*
Affiliation:
Università di Bologna
Iliyan Georgiev
Affiliation:
Universidade Nova de Lisboa
*
*Address correspondence to Giuseppe Cavaliere, Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, I-40126 Bologna, Italy; e-mail: giuseppe.cavaliere@unibo.it.
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Abstract

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We consider estimation and testing in finite-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., those 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 that ensure that (i) the dummy-based estimator is consistent at higher rates than the ordinary least squares 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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 6 , December 2013, pp. 1162 - 1195
Copyright
Copyright © Cambridge University Press 2013 

Footnotes

We thank Pentti Saikkonen the (co-editor), three anonymous referees, and Keith Knight for their very useful comments. Support was provided by the Fundação para a Ciência e a Tecnologia, Portugal, through grants PTDC/EGEECO/108620/2008. Cavaliere also thanks the Danish Council for Independent Research, Sapere Aude | DFF Advanced Grant (grant 12-124980) for financial support.

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