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Local explosion modelling by non-causal process

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  • Christian Gouriéroux
  • Jean-Michel Zakoïan

Abstract

The noncausal autoregressive process with heavy-tailed errors possesses a nonlinear causal dynamics, which allows for %unit root, local explosion or asymmetric cycles often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as the existence of higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behavior of a vector of sample autocorrelations is studied in a semi-parametric noncausal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided.
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  • Christian Gouriéroux & Jean-Michel Zakoïan, 2017. "Local explosion modelling by non-causal process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 737-756, June.
    • Handle: RePEc:bla:jorssb:v:79:y:2017:i:3:p:737-756
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    File URL: http://hdl.handle.net/10.1111/rssb.12193
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    Cited by:

    1. 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.
    2. 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.
    3. Frédéric BEC & Alain GUAY, 2020. "A simple unit root test consistent against any stationary alternative," Working Papers 2020-28, Center for Research in Economics and Statistics.
    4. Gourieroux, Christian & Jasiak, Joann, 2019. "Robust analysis of the martingale hypothesis," Econometrics and Statistics, Elsevier, vol. 9(C), pages 17-41.
    5. Davis, Richard A. & Song, Li, 2020. "Noncausal vector AR processes with application to economic time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 246-267.
    6. 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.
    7. Antonio Aguirre & Ignacio N. Lobato, 2024. "Evidence of non-fundamentalness in OECD capital stocks," Empirical Economics, Springer, vol. 67(2), pages 761-772, August.
    8. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    9. Funovits, Bernd, 2024. "Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation," Journal of Econometrics, Elsevier, vol. 241(2).
    10. Frederique Bec & Alain Guay, 2020. "A Simple Unit Root Test Consistent Against Any Stationary Alternative," Working Papers 20-20, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    11. 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.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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