 A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovationsStelios 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) Downloads: (external link) Related works: 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 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 |
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