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NEGATIVE POWERS OF INTEGRATED PROCESSES

Published online by Cambridge University Press:  30 April 2021

Neslihan Sakarya  and
Robert M. de Jong
Neslihan Sakarya*
Affiliation:
University of Essex
Robert M. de Jong
Affiliation:
Ohio State University
*
Author correspondence to Neslihan Sakarya, Department of Economics, University of Essex, Colchester, UK; e-mail: ns17003@essex.ac.uk.
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Abstract

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This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than $-$1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.

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Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 2 , April 2022 , pp. 339 - 369
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

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