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Stochastic unit-root bilinear processes

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Author Info

  • Christian Francq

    ()
    (GREMARS University Lille 3)

  • Svetlana Makarova

    (European University at St. Petersburg, CREST)

  • Jean-Michel Zakoïan

    (GREMARSUniversity Lille 3)

Abstract

A class of stochastic unit-root bilinear processes, allowing for GARCH-type effects with asymmetries, is studied. The volatility is not bounded away from zero and is minimum for non zero innovations, which are important differences with the standard GARCH. Necessary and sufficient conditions for the strict and second-order stationarity of the error process are given. The strictly stationary solution is shown to be strongly mixing under mild additional assumptions. It follows that, in this model, the standard (non-stochastic) unit-root tests of Phillips-Perron and Dickey-Fuller are asymptotically valid to detect the presence of a (stochastic) unit-root. The finite sample properties of these tests are studied via Monte Carlo experiments

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 63.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:63

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Keywords: Augmented Dickey-Fuller test; Bilinear processes;

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