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The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test

Published online by Cambridge University Press:  11 February 2009

Peter Burridge  and
Emmanuel Guerre
Peter Burridge
Affiliation:
University of Birmingham
Emmanuel Guerre
Affiliation:
Université P et M Curie
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Abstract

We derive the limit distribution of the number of crossings of a level by a random walk with continuously distributed increments, using a Brownian motion local time approximation. This complements the well-known result for the random walk on the integers. Use of the frequency of level crossings to test for a unit root is examined.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 4 , October 1996 , pp. 705 - 723
Copyright
Copyright © Cambridge University Press 1996

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