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Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors


  • Hecq, Alain
  • Issler, João Victor
  • Telg, Sean


The mixed autoregressive causal-noncausal model (MAR) has been proposed to estimate economic relationships involving explosive roots in their autoregressive part, as they have stationary forward solutions. In previous work, possible exogenous variables in economic relationships are substituted into the error term to ensure the univariate MAR structure of the variable of interest. To allow for the impact of exogenous fundamental variables directly, we instead consider a MARX representation which allows for the inclusion of strictly exogenous regressors. We develop the asymptotic distribution of the MARX parameters. We assume a Student's t-likelihood to derive closed form solutions of the corresponding standard errors. By means of Monte Carlo simulations, we evaluate the accuracy of MARX model selection based on information criteria. We investigate the influence of the U.S. exchange rate and the U.S. industrial production index on several commodity prices.

Suggested Citation

  • Hecq, Alain & Issler, João Victor & Telg, Sean, 2017. "Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors," MPRA Paper 80767, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:80767

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    References listed on IDEAS

    1. 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.
    2. Lanne, Markku & Luoto, Jani, 2013. "Autoregression-based estimation of the new Keynesian Phillips curve," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 561-570.
    3. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, Open Access Journal, vol. 5(4), pages 1-22, October.
    4. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2011. "Non‐Fundamentalness in Structural Econometric Models: A Review," International Statistical Review, International Statistical Institute, vol. 79(1), pages 16-47, April.
    5. Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time-series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, March.
    6. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    7. Henri Nyberg & Markku Lanne & Erkka Saarinen, 2012. "Does noncausality help in forecasting economic time series?," Economics Bulletin, AccessEcon, vol. 32(4), pages 2849-2859.
    8. 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.
    9. Pesaran, M. Hashem, 2015. "Time Series and Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780198759980.
    10. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    11. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
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    More about this item


    Mixed causal-noncausal process; non-Gaussian errors; identification; rational expectation models; commodity prices;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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