Exploiting infinite variance through Dummy Variables in non-stationary autoregressions

Cavaliere, Giuseppe ; Georgiev, Iliyan (2013) Exploiting infinite variance through Dummy Variables in non-stationary autoregressions. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 31. DOI 10.6092/unibo/amsacta/3633. In: Quaderni di Dipartimento. Serie Ricerche ISSN 1973-9346.
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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.

Abstract
Document type
Monograph (Working Paper)
Creators
CreatorsAffiliationORCID
Cavaliere, Giuseppe
Georgiev, Iliyan
Keywords
Autoregressive processes; Infinite variance; Dummy variables; Processi autoregressivi; Varianza infinita; Variabili dummy
Subjects
ISSN
1973-9346
DOI
Deposit date
14 Jan 2013 08:11
Last modified
29 Jan 2013 09:49
URI

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