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Identification of Mixed Causal-Noncausal Models in Finite Samples


  • Alain Hecq
  • Lenard Lieb
  • Sean Telg


Gouriéroux, C., and J.-M. Zakoían [2013] propose to use noncausal models to parsimoniously capture nonlinear features often observed in financial time series and in particular bubble phenomena. In order to distinguish causal autoregressive processes from purely noncausal or mixed causal-noncausal ones, one has to depart from the Gaussianity assumption on the error distribution. Financial (and to a large extent macroeconomic) data are characterized by large and sudden changes that cannot be captured by the Normal distribution, which explains why leptokurtic error distributions are often considered in empirical finance. By means of Monte Carlo simulations, this paper investigates the identification of mixed causal-noncausal models in finite samples for different values of the excess kurtosis of the error process. We compare the performance of the MLE, assuming a t-distribution, with that of the LAD estimator that we propose in this paper. Similar to Davis, R., K. Knight, and J. Liu [1992] we find that for infinite variance autoregressive processes both the MLE and LAD estimator converge faster. We further specify the general asymptotic normality results obtained in Andrews, B., F. Breidt, and R. Davis [2006] for the case of t-distributed and Laplacian distributed error terms. We first illustrate our analysis by estimating mixed causal-noncausal autoregressions to model the demand for solar panels in Belgium over the last decade. Then we look at the presence of potential noncausal components in daily realized volatility measures for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations.

Suggested Citation

  • Alain Hecq & Lenard Lieb & Sean Telg, 2016. "Identification of Mixed Causal-Noncausal Models in Finite Samples," Annals of Economics and Statistics, GENES, issue 123-124, pages 307-331.
  • Handle: RePEc:adr:anecst:y:2016:i:123-124:p:307-331
    DOI: 10.15609/annaeconstat2009.123-124.0307

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    Cited by:

    1. Christian Gourieroux & Joann Jasiak, 2021. "Generalized Covariance Estimator," Papers 2107.06979,
    2. Kramkov, Viacheslav & Maksimov, Andrey, 2020. "Loan market markups and noncausal autoregressions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 60, pages 48-69.
    3. Francesco Giancaterini & Alain Hecq, 2020. "Inference in mixed causal and noncausal models with generalized Student's t-distributions," Papers 2012.01888,, revised Nov 2022.
    4. Gianluca Cubadda & Alain Hecq & Sean Telg, 2019. "Detecting Co‐Movements in Non‐Causal Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 697-715, June.
    5. Marina Friedrich & Sébastien Fries & Michael Pahle & Ottmar Edenhofer, 2020. "Rules vs. Discretion in Cap-and-Trade Programs: Evidence from the EU Emission Trading System," CESifo Working Paper Series 8637, CESifo.
    6. Fries, Sébastien & Zakoian, Jean-Michel, 2019. "Mixed Causal-Noncausal Ar Processes And The Modelling Of Explosive Bubbles," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1234-1270, December.
    7. Hecq, Alain & Issler, João Victor & Telg, Sean, 2017. "Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors," MPRA Paper 80767, University Library of Munich, Germany.
    8. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, vol. 5(4), pages 1-22, October.
    9. Frédérique Bec & Heino Bohn Nielsen & Sarra Saïdi, 2020. "Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1413-1428, December.
    10. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    11. Alain Hecq & Li Sun, 2019. "Identification of Noncausal Models by Quantile Autoregressions," Papers 1904.05952,
    12. Jean-Baptiste MICHAU, 2019. "Helicopter Drops of Money under Secular Stagnation," Working Papers 2019-10, Center for Research in Economics and Statistics.

    More about this item


    Noncausal Models; Non-Gaussian Distributions; Realized Volatilities; Bubbles;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy


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