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On the Noninvertible Moving Average Time Series with Infinite Variance

Published online by Cambridge University Press:  11 February 2009

Ngai Hang Chan
Ngai Hang Chan
Affiliation:
Carnegie Mellon University
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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.

Type
Miscellanea
Information
Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 680 - 685
Copyright
Copyright © Cambridge University Press 1993

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