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Spectral estimation for mixed causal-noncausal autoregressive models

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  • Alain Hecq
  • Daniel Velásquez-Gaviria

Abstract

Mixed causal-noncausal autoregressive (MAR) processes driven by non Gaussian noise can replicate the non linear dynamics induced by local explosive episodes observed in financial bubbles. MAR models cannot be identified using second-order moments because they share spectral density with a set of different representations. In this study, we propose an identification and estimation method based on the third-order spectral density cumulant that can recover the complete probability structure of the errors without assuming any prior knowledge of the probability distribution function. Monte Carlo experiments demonstrated the estimation and identification performances. Furthermore, we illustrated the adequacy of our method through an empirical application to eight monthly commodity prices. The results show that MAR models can effectively capture the explosiveness and bubble phenomena generated in the commodities market.

Suggested Citation

  • Alain Hecq & Daniel Velásquez-Gaviria, 2025. "Spectral estimation for mixed causal-noncausal autoregressive models," Econometric Reviews, Taylor & Francis Journals, vol. 44(7), pages 939-962, August.
    • Handle: RePEc:taf:emetrv:v:44:y:2025:i:7:p:939-962
    DOI: 10.1080/07474938.2025.2465372
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    File URL: http://hdl.handle.net/10.1080/07474938.2025.2465372
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    Cited by:

    1. F. Blasques & S. J. Koopman & G. Mingoli & S. Telg, 2025. "A Novel Test for the Presence of Local Explosive Dynamics," Journal of Time Series Analysis, Wiley Blackwell, vol. 46(5), pages 966-980, September.
    2. 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.
    3. Tom'as del Barrio Castro & Alain Hecq & Sean Telg, 2026. "Seasonality in Mixed Causal-Noncausal Processes," Papers 2604.07040, arXiv.org.
    4. Gianluca Cubadda & Francesco Giancaterini & Stefano Grassi, 2025. "Sequential Monte Carlo for Noncausal Processes," Papers 2501.03945, arXiv.org.
    5. Alain Hecq & Daniel Velasquez-Gaviria, 2023. "Spectral identification and estimation of mixed causal-noncausal invertible-noninvertible models," Papers 2310.19543, arXiv.org.
    6. Aryan Manafi Neyazi, 2025. "Generalized Covariance Estimator under Misspecification and Constraints," Papers 2509.13492, arXiv.org.

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