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Mixed causal–noncausal autoregressions with exogenous regressors

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  • Alain Hecq
  • Joao Victor Issler
  • Sean Telg

Abstract

Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non‐Gaussian densities. For a Student t likelihood, closed‐form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices.

Suggested Citation

  • Alain Hecq & Joao Victor Issler & Sean Telg, 2020. "Mixed causal–noncausal autoregressions with exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(3), pages 328-343, April.
    • Handle: RePEc:wly:japmet:v:35:y:2020:i:3:p:328-343
    DOI: 10.1002/jae.2751
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    Cited by:

    1. Giancaterini, Francesco & Hecq, Alain, 2025. "Inference in mixed causal and noncausal models with generalized Student’s t-distributions," Econometrics and Statistics, Elsevier, vol. 33(C), pages 1-12.
    2. Cleiton Guollo Taufemback, 2023. "Non‐parametric short‐ and long‐run Granger causality testing in the frequency domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 69-92, January.
    3. Frédérique Bec & Alain Guay & Heino Bohn Nielsen & Sarra Saïdi, 2022. "Power of unit root tests against nonlinear and noncausal alternatives," Thema Working Papers 2022-14, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    4. 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.
    5. 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.
    6. Hecq, Alain & Issler, João Victor & Voisin, Elisa, 2024. "A short term credibility index for central banks under inflation targeting: An application to Brazil," Journal of International Money and Finance, Elsevier, vol. 143(C).
    7. 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.
    8. Hecq Alain & Sun Li, 2021. "Selecting between causal and noncausal models with quantile autoregressions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(5), pages 393-416, December.
    9. Juan D. Borrero & Jesus Mariscal, 2022. "Predicting Time SeriesUsing an Automatic New Algorithm of the Kalman Filter," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    10. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.
    11. Viacheslav Kramkov & Andrey Maksimov, 2020. "Loan market markups and noncausal autoregressions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 60, pages 48-69.
    12. Aryan Manafi Neyazi, 2025. "Generalized Covariance Estimator under Misspecification and Constraints," Papers 2509.13492, arXiv.org.

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