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STOCHASTIC UNIT ROOT MODELS

Published online by Cambridge University Press:  03 November 2006

Christian Gourieroux  and
Christian Y. Robert
Christian Gourieroux
Affiliation:
University of Toronto CREST and CEPREMAP
Christian Y. Robert
Affiliation:
CNAM and CREST
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Abstract

This paper develops a dynamic switching model, with a random walk and a stationary regime, where the time spent in the random walk regime is endogeneously predetermined. More precisely, we assume that the process is recursively defined by Yt = μ + Yt−1 + εt, with stochastic probability πrw(Yt−1), Yt = μ + εt, with stochastic probability 1 − πrw(Yt−1), where (εt) is a strong white noise and πrw is a nondecreasing function. Then, the dynamics of the process (Yt), its marginal distribution, and the distribution of the time spent in the unit root regime depend on the pattern of random walk intensity πrw and on the noise distribution F. Moreover, we study the links between the endogeneous switching regime and the degree of persistence of the process (Yt).

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1052 - 1090
Copyright
© 2006 Cambridge University Press

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