A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovations
Stelios Arvanitis
Statistics & Probability Letters, 2017, vol. 126, issue C, 198-204
Abstract:
We are occupied with the limit theory of the OLSE and of a subsequent Dickey–Fuller test when the unit root process has heavy tailed and dependent innovations that do not possess moments of order α for some α∈0,2. The innovation process has the form of a “martingale-type” transform constructed as a pointwise product between an iid sequence in the domain of attraction of an α stable distribution with a non existing α moment, for some α∈0,2, and a positive scaling mixing sequence that has a slowly varying at infinity truncated α moment. We derive a functional limit theorem with complex rates and limits that depend on Levy α-stable processes. The OLSE remains superconsistent with rate n, and the limiting distribution is a functional of the previous process. When α=2 we recover the standard Dickey–Fuller distribution.
Keywords: Unit root process; Dickey–Fuller test; Martingale transform; Levy stable process; Marcinkiewicz LLN; Slowly varying sequences (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715217300883
Full text for ScienceDirect subscribers only
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:eee:stapro:v:126:y:2017:i:c:p:198-204
Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01
DOI: 10.1016/j.spl.2017.02.032
Access Statistics for this article
Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul
More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().