Robust inference in conditionally heteroskedastic autoregressions

Rasmus Søndergaard Pedersen

MPRA Paper from University Library of Munich, Germany

Abstract: We consider robust inference for an autoregressive parameter in a stationary autoregressive model with GARCH innovations when estimation is based on least squares estimation. As the innovations exhibit GARCH, they are by construction heavy-tailed with some tail index $\kappa$. The rate of consistency as well as the limiting distribution of the least squares estimator depend on $\kappa$. In the spirit of Ibragimov and Müller (“t-statistic based correlation and heterogeneity robust inference”, Journal of Business & Economic Statistics, 2010, vol. 28, pp. 453-468), we consider testing a hypothesis about a parameter based on a Student’s t-statistic for a fixed number of subsamples of the original sample. The merit of this approach is that no knowledge about the value of $\kappa$ nor about the rate of consistency and the limiting distribution of the least squares estimator is required. We verify that the one-sided t-test is asymptotically a level $\alpha$ test whenever $\alpha \le $ 5% uniformly over $\kappa \ge 2$, which includes cases where the innovations have infinite variance. A simulation experiment suggests that the finite-sample properties of the test are quite good.

Keywords: t-test; AR-GARCH; regular variation; least squares estimation (search for similar items in EconPapers)
JEL-codes: C12 C22 C46 C51 (search for similar items in EconPapers)
Date: 2017-10-04
New Economics Papers: this item is included in nep-cta, nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/81979/1/MPRA_paper_81979.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/90609/8/MPRA_paper_90609.pdf revised version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:81979

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().