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

作者：Arvanitis Stelios^*

来源：Statistics & Probability Letters, 2017, 126: 198-204.

DOI：10.1016/j.spl.2017.02.032

• Unit root process
• Dickey-Fuller test
• Martingale transform
• Levy stable process
• Marcinkiewicz LLN
• Slowly varying sequences

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 alpha for some alpha is an element of (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 a stable distribution with a non existing alpha moment, for some alpha is an element of(0, 2], and a positive scaling mixing sequence that has a slowly varying at infinity truncated alpha moment. We derive a functional limit theorem with complex rates and limits that depend on Levy a-stable processes. The OLSE remains superconsistent with rate n, and the limiting distribution is a functional of the previous process. When alpha = 2 we recover the standard Dickey Fuller distribution.

• 出版日期2017-7