On the noninvertible moving average time series with infinite variance

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Original languageEnglish
Pages (from-to)680-685
Journal / PublicationEconometric Theory
Volume9
Issue number4
Publication statusPublished - Aug 1993
Externally publishedYes

Abstract

The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the innovation and the stable index α. This result enables one to perform asymptotic testing for the presence of a unit root for a noninvertible moving average model through the constructed derived process under the null hypothesis. It provides not only a parallel analog of its autoregressive counterparts, but also a useful alternative to determine “over-differencing” for time series that exhibit heavy-tailed phenomena. © 1993, Cambridge University Press. All rights reserved.

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