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A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovations

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  • Arvanitis, Stelios

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.

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  • Arvanitis, Stelios, 2017. "A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovations," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 198-204.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:198-204
    DOI: 10.1016/j.spl.2017.02.032
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