IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v172y2013i2p222-234.html
   My bibliography  Save this article

Model identification for infinite variance autoregressive processes

Author

Listed:
  • Andrews, Beth
  • Davis, Richard A.

Abstract

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.

Suggested Citation

  • Andrews, Beth & Davis, Richard A., 2013. "Model identification for infinite variance autoregressive processes," Journal of Econometrics, Elsevier, vol. 172(2), pages 222-234.
    • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:222-234
    DOI: 10.1016/j.jeconom.2012.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612001935
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2012.08.009?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. Gallagher, Colin M., 2001. "A method for fitting stable autoregressive models using the autocovariation function," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 381-390, July.
    2. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    3. 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.
    4. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    5. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    6. 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.
    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. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    2. 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.
    3. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    4. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    5. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    6. Kindop, Igor, 2021. "Ubiquitous multimodality in mixed causal-noncausal processes," MPRA Paper 109594, University Library of Munich, Germany, revised 04 Sep 2021.
    7. 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.
    8. Fries, Sébastien & Zakoian, Jean-Michel, 2019. "Mixed Causal-Noncausal Ar Processes And The Modelling Of Explosive Bubbles," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1234-1270, December.
    9. Amit Shelef & Edna Schechtman, 2019. "A Gini-based time series analysis and test for reversibility," Statistical Papers, Springer, vol. 60(3), pages 687-716, June.
    10. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.

    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. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    2. 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.
    3. 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.
    4. 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.
    5. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    6. Hecq, A.W. & Lieb, L.M. & Telg, J.M.A., 2015. "Identification of Mixed Causal-Noncausal Models : How Fat Should We Go?," Research Memorandum 035, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Hecq, Alain & Issler, João Victor & Telg, Sean, 2017. "Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors," MPRA Paper 80767, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. 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.
    11. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    12. Alain Hecq & Li Sun, 2019. "Identification of Noncausal Models by Quantile Autoregressions," Papers 1904.05952, arXiv.org.
    13. 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.
    14. Lanne Markku, 2015. "Noncausality and inflation persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 469-481, September.
    15. 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.
    16. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    17. Xinghui Wang & Shuhe Hu, 2017. "Asymptotics of self-weighted M-estimators for autoregressive models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 83-92, January.
    18. Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    19. 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.
    20. Lanne, Markku & Saikkonen, Pentti, 2008. "Modeling Expectations with Noncausal Autoregressions," MPRA Paper 8411, University Library of Munich, Germany.

    More about this item

    Keywords

    Akaike’s information criterion; All-pass models; Autoregressive processes; Infinite variance; Noncausal;
    All these keywords.

    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

    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:172:y:2013:i:2:p:222-234. 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.