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Explosive Bubble Modelling by Noncausal Process


  • Christian Gouriéroux

    () (CREST and University of Toronto)

  • Jean-Michel Zakoian

    () (CREST and University Lille 3)


The linear mixed causal and noncausal autoregressive processes provide often a better fit to economic and financial time series than the standard causal linear autoregressive processes. By considering the example of the noncausal Cauchy autoregressive process, we show that it might be explained by the special associated nonlinear causal dynamics. Indeed, this causal dynamics can include unit root, bubble phenomena, or asymmetric cycles often observed on financial markets. The noncausal Cauchy autoregressive process provides a new modelling for explosive multiple bubbles and their transmission in a multivariate dynamic framework. We also explain why standard unit root tests will fail in detecting such explosive bubbles

Suggested Citation

  • Christian Gouriéroux & Jean-Michel Zakoian, 2013. "Explosive Bubble Modelling by Noncausal Process," Working Papers 2013-04, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-04

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    Cited by:

    1. repec:gam:jecnmx:v:5:y:2017:i:4:p:47-:d:115992 is not listed on IDEAS
    2. Christian Gourieroux & Joann Jasiak, 2016. "Filtering, Prediction and Simulation Methods for Noncausal Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 405-430, May.
    3. Christian Gouriéroux & Jean-Michel Zakoïan, 2015. "On Uniqueness of Moving Average Representations of Heavy-tailed Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 876-887, November.
    4. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    5. Andras Fulop & Jun Yu, 2017. "Bayesian Analysis of Bubbles in Asset Prices," Econometrics, MDPI, Open Access Journal, vol. 5(4), pages 1-23, October.

    More about this item


    Causal Innovation; Explosive Bubble; Noncausal Process; Unit Root; Bubble Cointegration;

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