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dc.contributor.authorBarreto-Souza, Wagner
dc.contributor.authorChan, Ngai Hang
dc.date.accessioned2021-07-26T11:10:04Z
dc.date.available2021-07-26T11:10:04Z
dc.date.issued2021-07-16
dc.identifier.urihttp://hdl.handle.net/10754/670273
dc.description.abstractThis paper introduces a Nearly Unstable INteger-valued AutoRegressive Conditional Heteroskedasticity (NU-INARCH) process for dealing with count time series data. It is proved that a proper normalization of the NU-INARCH process endowed with a Skorohod topology weakly converges to a Cox-Ingersoll-Ross diffusion. The asymptotic distribution of the conditional least squares estimator of the correlation parameter is established as a functional of certain stochastic integrals. Numerical experiments based on Monte Carlo simulations are provided to verify the behavior of the asymptotic distribution under finite samples. These simulations reveal that the nearly unstable approach provides satisfactory and better results than those based on the stationarity assumption even when the true process is not that close to non-stationarity. A unit root test is proposed and its Type-I error and power are examined via Monte Carlo simulations. As an illustration, the proposed methodology is applied to the daily number of deaths due to COVID-19 in the United Kingdom.
dc.description.sponsorshipResearch supported in part by grants from the KAUST and NIH 1R01EB028753-01 (W. Barreto-Souza), HKSAR-RGC-GRF No. 14325216 and the Theme-based Research Scheme of HKSAR-RGC-TBS T32- 101/15-R (N.H. Chan).
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2107.07963.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectCount time series
dc.subjectCox-Ingersoll-Ross diffusion process
dc.subjectInference
dc.subjectLimit theorems
dc.subjectStochastic integral.
dc.titleNearly Unstable Integer-Valued ARCH Process and Unit Root Testing
dc.typePreprint
dc.contributor.departmentStatistics Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Statistics, The Chinese University of Hong Kong, Hong Kong
dc.identifier.arxivid2107.07963
kaust.personBarreto-Souza, Wagner


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