The University of Southampton
University of Southampton Institutional Repository

Mildly explosive autoregression under stationary conditional heteroskedasticity

Mildly explosive autoregression under stationary conditional heteroskedasticity
Mildly explosive autoregression under stationary conditional heteroskedasticity
A limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or stochastic volatility models. No mixing conditions nor moments of higher order than 2 are assumed for the innovation process. As in Magdalinos (2012), we find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the form of the limiting distribution and, in the case of long range dependence, the rate of convergence, while conditional heteroskedasticity affects only the asymptotic variance. These effects are cancelled out in least squares regression theory and thereby the Cauchy limit theory of Phillips and Magdalinos (2007a) remains invariant to a wide class of stationary conditionally heteroskedastic innovations processes.
0143-9782
892-908
Arvanitis, Stelios
4a4a4f52-423b-4371-9337-1445bc4703f2
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Arvanitis, Stelios
4a4a4f52-423b-4371-9337-1445bc4703f2
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31

Arvanitis, Stelios and Magdalinos, Tassos (2018) Mildly explosive autoregression under stationary conditional heteroskedasticity. Journal of Time Series Analysis, 39 (6), 892-908. (doi:10.1111/jtsa.12410).

Record type: Article

Abstract

A limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or stochastic volatility models. No mixing conditions nor moments of higher order than 2 are assumed for the innovation process. As in Magdalinos (2012), we find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the form of the limiting distribution and, in the case of long range dependence, the rate of convergence, while conditional heteroskedasticity affects only the asymptotic variance. These effects are cancelled out in least squares regression theory and thereby the Cauchy limit theory of Phillips and Magdalinos (2007a) remains invariant to a wide class of stationary conditionally heteroskedastic innovations processes.

Text
AM2 Magdalinos - Accepted Manuscript
Download (219kB)

More information

Submitted date: 2018
Accepted/In Press date: 31 May 2018
e-pub ahead of print date: 1 July 2018
Published date: November 2018

Identifiers

Local EPrints ID: 420957
URI: http://eprints.soton.ac.uk/id/eprint/420957
ISSN: 0143-9782
PURE UUID: 96b9c970-4780-40b1-970e-8e8cd0c5a0d8

Catalogue record

Date deposited: 18 May 2018 16:31
Last modified: 20 Jan 2020 17:30

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×