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THE SUM OF THE RECIPROCAL OF THE RANDOM WALK

Published online by Cambridge University Press:  13 February 2019

Jon Michel  and
Robert de Jong
Jon Michel*
Affiliation:
Ohio State University
Robert de Jong
Affiliation:
Ohio State University
*
*Address correspondence to Jon Michel, Department of Economics, Ohio State University, 304 Arps Hall, Columbus, OH 43210, USA; e-mail: michel.82@osu.edu.
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Abstract

This paper derives the limit distribution of the rescaled sum of the reciprocal of the positive part of a random walk with continuously distributed innovations, and of the rescaled sum of the reciprocal of the absolute value of a random walk with continuously distributed innovations. It also considers this statistic for the case of a simple random walk, and shows that the limit distribution is different for this case.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 1 , February 2020 , pp. 170 - 183
Copyright
Copyright © Cambridge University Press 2019 

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Footnotes

We would like to thank the Editor (Peter C.B. Phillips), Co-Editor (Benedikt Pötscher), and two anonymous referees for numerous useful comments and suggestions.

References

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