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Forecasting bubbles with mixed causal-noncausal autoregressive models

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  • Hecq, Alain
  • Voisin, Elisa

Abstract

Density forecasts of locally explosive processes are investigated using mixed causal-noncausal models, namely time series models with both lag and lead components. In the absence of theoretical expressions for the predictive density for a large range of potential error distributions, two approximation methods are analysed and compared using Monte Carlo simulations. The focus is on the prediction of one-step ahead probabilities of turning points during bubble episodes. A thorough analysis provides some guidance in using these approximation methods during extreme events, with the suggestion to consider both approaches together as they jointly carry more information. The analysis is illustrated with an application on Nickel prices, focusing on the financial crisis bubble.

Suggested Citation

  • Hecq, Alain & Voisin, Elisa, 2021. "Forecasting bubbles with mixed causal-noncausal autoregressive models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 29-45.
    • Handle: RePEc:eee:ecosta:v:20:y:2021:i:c:p:29-45
    DOI: 10.1016/j.ecosta.2020.03.007
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    1. Christian Gouriéroux & Joann Jasiak & Alain Monfort, 2016. "Stationary Bubble Equilibria in Rational Expectation Models," Working Papers 2016-31, Centre de Recherche en Economie et Statistique.
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    3. 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.
    4. 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.
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    9. 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.
    10. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2012. "Optimal forecasting of noncausal autoregressive time series," International Journal of Forecasting, Elsevier, vol. 28(3), pages 623-631.
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    13. Karapanagiotidis, Paul, 2014. "Dynamic modeling of commodity futures prices," MPRA Paper 56805, University Library of Munich, Germany.
    14. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    15. 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.
    16. Lof, Matthijs & Nyberg, Henri, 2017. "Noncausality and the commodity currency hypothesis," Energy Economics, Elsevier, vol. 65(C), pages 424-433.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Weifeng Jin, 2023. "Quantile Autoregression-based Non-causality Testing," Papers 2301.02937, arXiv.org.
    2. Francisco Blasques & Siem Jan Koopman & Gabriele Mingoli, 2023. "Observation-Driven filters for Time-Series with Stochastic Trends and Mixed Causal Non-Causal Dynamics," Tinbergen Institute Discussion Papers 23-065/III, Tinbergen Institute.
    3. Alain Hecq & Joao Issler & Elisa Voisin, 2022. "A short term credibility index for central banks under inflation targeting: an application to Brazil," Papers 2205.00924, arXiv.org, revised Jul 2022.
    4. Alain Hecq & Elisa Voisin, 2023. "Predicting Crashes in Oil Prices During The Covid-19 Pandemic with Mixed Causal-Noncausal Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 209-233, Emerald Group Publishing Limited.
    5. Francesco Giancaterini & Alain Hecq, 2020. "Inference in mixed causal and noncausal models with generalized Student's t-distributions," Papers 2012.01888, arXiv.org, revised Nov 2022.
    6. 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.
    7. Christian Gourieroux & Joann Jasiak & Michelle Tong, 2021. "Convolution‐based filtering and forecasting: An application to WTI crude oil prices," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(7), pages 1230-1244, November.
    8. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    9. Alain Hecq & Daniel Velasquez-Gaviria, 2022. "Spectral estimation for mixed causal-noncausal autoregressive models," Papers 2211.13830, arXiv.org.
    10. Gianluca Cubadda & Francesco Giancaterini & Alain Hecq & Joann Jasiak, 2023. "Optimization of the Generalized Covariance Estimator in Noncausal Processes," Papers 2306.14653, arXiv.org, revised Jan 2024.

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    More about this item

    Keywords

    Noncausal models; Forecasting; Predictive densities; Bubbles; Simulations-based forecasts;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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