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Stochastic unit-root bilinear processes


  • Christian Francq

    () (GREMARS University Lille 3)

  • Svetlana Makarova

    (European University at St. Petersburg, CREST)

  • Jean-Michel Zakoïan

    (GREMARSUniversity Lille 3)


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

Suggested Citation

  • Christian Francq & Svetlana Makarova & Jean-Michel Zakoïan, 2006. "Stochastic unit-root bilinear processes," Computing in Economics and Finance 2006 63, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:63

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    More about this item


    Augmented Dickey-Fuller test; Bilinear processes;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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