IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v13y2009i2n5.html
   My bibliography  Save this article

Discovering Hidden Structures Using Mixture Models: Application to Nonlinear Time Series Processes

Author

Listed:
  • Shahbaba Babak

    (University of California, Irvine)

Abstract

This paper discuses the application of mixture models for analyzing data with hidden structure. More specifically, we are interested in situations where the structure is due to some unobserved factors. Detecting the latent structures in data is not trivial. On the other hand, since such structures could obscure the effect of the observed variables, ignoring them (e.g., using simple linear models) could result in wrong inference. To address this issue, we propose to use Dirichlet process mixtures. In this approach, the mixture identifier (i.e., the latent variable that assigns each component to a data point) acts as a surrogate for possible missing factors and provides insight into possible hidden structure in the data. An illustrative example is provided to show the usefulness of this approach. We also discuss the application of our method for analyzing time series processes that are subject to regime changes where there is no specific economic theory about the structure of the model.

Suggested Citation

  • Shahbaba Babak, 2009. "Discovering Hidden Structures Using Mixture Models: Application to Nonlinear Time Series Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-21, May.
    • Handle: RePEc:bpj:sndecm:v:13:y:2009:i:2:n:5
    DOI: 10.2202/1558-3708.1609
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1609
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1609?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. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    2. Cao, C Q & Tsay, R S, 1992. "Nonlinear Time-Series Analysis of Stock Volatilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 165-185, Suppl. De.
    3. Burgess, S M, 1992. "Nonlinear Dynamics in a Structural Model of Employment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 101-118, Suppl. De.
    4. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    5. Rothman, Philip, 1991. "Further evidence on the asymmetric behavior of unemployment rates over the business cycle," Journal of Macroeconomics, Elsevier, vol. 13(2), pages 291-298.
    6. Krolzig, Hans-Martin, 2001. "Business cycle measurement in the presence of structural change: international evidence," International Journal of Forecasting, Elsevier, vol. 17(3), pages 349-368.
    7. Enders Walter & Falk Barry L & Siklos Pierre, 2007. "A Threshold Model of Real U.S. GDP and the Problem of Constructing Confidence Intervals in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-28, September.
    8. Hansen Bruce E., 1997. "Inference in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-16, April.
    9. Bruce Hansen, 1999. "Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-576, December.
    10. Strikholm, Birgit & Teräsvirta, Timo, 2005. "Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions," SSE/EFI Working Paper Series in Economics and Finance 578, Stockholm School of Economics, revised 11 Feb 2005.
    11. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    12. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    Full references (including those not matched with items on IDEAS)

    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. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    2. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    3. Pitarakis Jean-Yves, 2006. "Model Selection Uncertainty and Detection of Threshold Effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-30, March.
    4. Emilio Zanetti Chini, 2013. "Generalizing smooth transition autoregressions," CREATES Research Papers 2013-32, Department of Economics and Business Economics, Aarhus University.
    5. Pitarakis Jean-Yves, 2006. "Model Selection Uncertainty and Detection of Threshold Effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-30, March.
    6. Pitarakis, J., 2004. "Model selection uncertainty and detection of threshold effects," Discussion Paper Series In Economics And Econometrics 0409, Economics Division, School of Social Sciences, University of Southampton.
    7. Rinke, Saskia, 2016. "The Influence of Additive Outliers on the Performance of Information Criteria to Detect Nonlinearity," Hannover Economic Papers (HEP) dp-575, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    8. Birgit Strikholm & Timo Teräsvirta, 2006. "A sequential procedure for determining the number of regimes in a threshold autoregressive model," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 472-491, November.
    9. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    10. Jens‐Peter Loy & Dieter Pennerstorfer & Daniela Rroshi & Christoph Weiss & Biliana Yontcheva, 2022. "Consumer Information and Price Transmission: Empirical Evidence," Journal of Industrial Economics, Wiley Blackwell, vol. 70(3), pages 631-683, September.
    11. Camilo Alberto Cárdenas-Hurtado & Aaron Levi Garavito-Acosta & Jorge Hernán Toro-Córdoba, 2018. "Asymmetric Effects of Terms of Trade Shocks on Tradable and Non-tradable Investment Rates: The Colombian Case," Borradores de Economia 1043, Banco de la Republica de Colombia.
    12. Singh, Tarlok, 2014. "On the regime-switching and asymmetric dynamics of economic growth in the OECD countries," Research in Economics, Elsevier, vol. 68(2), pages 169-192.
    13. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, January.
    14. Martinez Oscar & Olmo Jose, 2012. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-39, September.
    15. Pérez-Alonso Alicia & Di Sanzo Silvestro, 2010. "Unemployment and Hysteresis: A Nonlinear Unobserved Components Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-29, December.
    16. Dijk, Dick van & Franses, Philip Hans, 1999. "Modeling Multiple Regimes in the Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 3(3), pages 311-340, September.
    17. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    18. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    19. Kulaksizoglu, Tamer & Kulaksizoglu, Sebnem, 2009. "The U.S. Excess Money Growth and Inflation Relation in the Long-Run: A Nonlinear Analysis," MPRA Paper 23780, University Library of Munich, Germany.
    20. Luigi Grossi & Fany Nan, 2018. "The influence of renewables on electricity price forecasting: a robust approach," Working Papers 2018/10, Institut d'Economia de Barcelona (IEB).

    More about this item

    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:bpj:sndecm:v:13:y:2009:i:2:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.