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Stochastic unit-root bilinear processes

Author

Listed:
  • 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

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
    as

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    References listed on IDEAS

    as
    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, December.
    2. Orphanides, Athanasios, 2004. "Monetary Policy Rules, Macroeconomic Stability, and Inflation: A View from the Trenches," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(2), pages 151-175, April.
    3. Clarida, Richard & Gali, Jordi & Gertler, Mark, 1998. "Monetary policy rules in practice Some international evidence," European Economic Review, Elsevier, vol. 42(6), pages 1033-1067, June.
    4. Oscar Landerretche & Felipe Morandé & Klaus Schmidt-Hebbe, 1999. "Inflation Targets and Stabilization in Chile," Working Papers Central Bank of Chile 55, Central Bank of Chile.
    5. Jansson, Per & Vredin, Anders, 2003. "Forecast-Based Monetary Policy: The Case of Sweden," International Finance, Wiley Blackwell, vol. 6(3), pages 349-380, Winter.
    6. Kenneth N. Kuttner, 2004. "The role of policy rules in inflation targeting," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 89-112.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    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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