IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v216y2020i1p246-267.html
   My bibliography  Save this article

Noncausal vector AR processes with application to economic time series

Author

Listed:
  • Davis, Richard A.
  • Song, Li

Abstract

Inference procedures for noncausal autoregressive (AR) models have been well studied and applied in a variety of applications from environmental to financial. For such processes, the observation at time t may depend on both past and future shocks in the system. In this paper, we consider extension of the univariate noncausal AR models to the vector AR (VAR) case. The extension presents several interesting challenges since even a first-order VAR can possess both causal and noncausal components. Assuming a non-Gaussian distribution for the noise, we show how to compute an approximation to the likelihood function. Under suitable conditions, it is shown that the maximum likelihood estimator (MLE) of the vector of AR parameters is asymptotically normal. The estimation procedure is illustrated with a simulation study for a VAR(1) process and with two real data examples.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:216:y:2020:i:1:p:246-267
    DOI: 10.1016/j.jeconom.2020.01.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620300221
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2020.01.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    2. Tiao, George C & Tsay, Ruey S, 1983. "Multiple Time Series Modeling and Extended Sample Cross-Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 43-56, January.
    3. Andrew Mountford & Harald Uhlig, 2009. "What are the effects of fiscal policy shocks?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 960-992.
    4. 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.
    5. F. J. Breidt & R. A. Davis, 1992. "Time‐Reversibility, Identifiability And Independence Of Innovations For Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(5), pages 377-390, September.
    6. Lanne, Markku & Saikkonen, Pentti, 2008. "Modeling Expectations with Noncausal Autoregressions," MPRA Paper 8411, University Library of Munich, Germany.
    7. 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.
    8. Richard A. Davis & Jing Zhang, 2018. "Semi†Parametric Estimation for Non†Gaussian Non†Minimum Phase ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(3), pages 251-272, May.
    9. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    10. Kung-Sik Chan & Lop-Hing Ho & Howell Tong, 2006. "A note on time-reversibility of multivariate linear processes," Biometrika, Biometrika Trust, vol. 93(1), pages 221-227, March.
    11. repec:zbw:bofrdp:2009_018 is not listed on IDEAS
    12. 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.
    13. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2020. "Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 55-67, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Numan Ülkü & Kexing Wu, 2023. "Stock Market's Response to Real Output Shocks in China: A VARwAL Estimation," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 31(5), pages 1-25, September.
    2. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    3. 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.
    4. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    5. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.
    6. Xuanling Yang & Dong Li & Ting Zhang, 2024. "A simple stochastic nonlinear AR model with application to bubble," Papers 2401.07038, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    3. 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.
    4. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    5. 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.
    6. Gourieroux, Christian & Jasiak, Joann, 2017. "Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation," Journal of Econometrics, Elsevier, vol. 200(1), pages 118-134.
    7. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    8. Markku Lanne & Arto Luoma & Jani Luoto, 2012. "Bayesian Model Selection And Forecasting In Noncausal Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 812-830, August.
    9. 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.
    10. Lanne Markku, 2015. "Noncausality and inflation persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 469-481, September.
    11. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    12. 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.
    13. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    14. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    15. Karapanagiotidis, Paul, 2014. "Dynamic modeling of commodity futures prices," MPRA Paper 56805, University Library of Munich, Germany.
    16. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    17. Karapanagiotidis, Paul, 2013. "Empirical evidence for nonlinearity and irreversibility of commodity futures prices," MPRA Paper 56801, University Library of Munich, Germany.
    18. 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.
    19. 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.
    20. repec:zbw:bofrdp:2013_026 is not listed on IDEAS
    21. repec:zbw:bofrdp:2009_018 is not listed on IDEAS
    22. Markku Lanne & Pentti Saikkonen, 2011. "GMM Estimation with Non‐causal Instruments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 581-592, October.

    More about this item

    Keywords

    Vector autoregressive model; Noncausal; Non-Gaussian;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:216:y:2020:i:1:p:246-267. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.