IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v112y2017i517p424-435.html
   My bibliography  Save this article

Shrinkage Estimation for Multivariate Hidden Markov Models

Author

Listed:
  • Mark Fiecas
  • Jürgen Franke
  • Rainer von Sachs
  • Joseph Tadjuidje Kamgaing

Abstract

Motivated from a changing market environment over time, we consider high-dimensional data such as financial returns, generated by a hidden Markov model that allows for switching between different regimes or states. To get more stable estimates of the covariance matrices of the different states, potentially driven by a number of observations that are small compared to the dimension, we modify the expectation–maximization (EM) algorithm so that it yields the shrinkage estimators for the covariance matrices. The final algorithm turns out to reproduce better estimates not only for the covariance matrices but also for the transition matrix. It results into a more stable and reliable filter that allows for reconstructing the values of the hidden Markov chain. In addition to a simulation study performed in this article, we also present a series of theoretical results that include dimensionality asymptotics and provide the motivation for certain techniques used in the algorithm. Supplementary materials for this article are available online.

Suggested Citation

  • Mark Fiecas & Jürgen Franke & Rainer von Sachs & Joseph Tadjuidje Kamgaing, 2017. "Shrinkage Estimation for Multivariate Hidden Markov Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 424-435, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:424-435
    DOI: 10.1080/01621459.2016.1148608
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2016.1148608
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2016.1148608?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Christian Francq & Michel Roussignol, 1997. "On White Noises Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(6), pages 553-578, November.
    3. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    4. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    5. J. Franke & J.-P. Stockis & J. Tadjuidje-Kamgaing & W. Li, 2011. "Mixtures of nonparametric autoregressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 287-303.
    6. Jean‐Pierre Stockis & Jürgen Franke & Joseph Tadjuidje Kamgaing, 2010. "On geometric ergodicity of CHARME models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 141-152, May.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    8. Bhm, Hilmar & von Sachs, Rainer, 2009. "Shrinkage estimation in the frequency domain of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 913-935, May.
    9. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
    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. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    2. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Marcelo Lewin & Carlos Heitor Campani, 2023. "Constrained portfolio strategies in a regime-switching economy," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 27-59, March.
    4. Peter Nystrup & Stephen Boyd & Erik Lindström & Henrik Madsen, 2019. "Multi-period portfolio selection with drawdown control," Annals of Operations Research, Springer, vol. 282(1), pages 245-271, November.
    5. Reetam Majumder & Qing Ji & Nagaraj K. Neerchal, 2023. "Optimal Stock Portfolio Selection with a Multivariate Hidden Markov Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 177-198, May.
    6. David Hallac & Peter Nystrup & Stephen Boyd, 2019. "Greedy Gaussian segmentation of multivariate time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 727-751, September.

    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. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    2. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    3. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    4. Sumanjay Dutta & Shashi Jain, 2023. "Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation," Papers 2305.11298, arXiv.org.
    5. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    6. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    7. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    9. Abdoulkarim Ilmi Amir & Yacouba Boubacar Maïnassara, 2020. "Multivariate portmanteau tests for weak multiplicative seasonal VARMA models," Statistical Papers, Springer, vol. 61(6), pages 2529-2560, December.
    10. Avagyan, Vahe & Nogales, Francisco J., 2014. "Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix," DES - Working Papers. Statistics and Econometrics. WS ws141208, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Xingqi Du & Subhashis Ghosal, 2018. "Bayesian Discriminant Analysis Using a High Dimensional Predictor," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 112-145, December.
    13. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    14. repec:cte:wsrepe:24534 is not listed on IDEAS
    15. Amendola, Alessandra & Christian, Francq, 2009. "Concepts and tools for nonlinear time series modelling," MPRA Paper 15140, University Library of Munich, Germany.
    16. Jianqing Fan & Ricardo Masini & Marcelo C. Medeiros, 2021. "Bridging factor and sparse models," Papers 2102.11341, arXiv.org, revised Sep 2022.
    17. Liang, Wanfeng & Ma, Xiaoyan, 2024. "A new approach for ultrahigh-dimensional covariance matrix estimation," Statistics & Probability Letters, Elsevier, vol. 204(C).
    18. Banerjee, Sayantan & Akbani, Rehan & Baladandayuthapani, Veerabhadran, 2019. "Spectral clustering via sparse graph structure learning with application to proteomic signaling networks in cancer," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 46-69.
    19. Avagyan, Vahe & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Zamar, Rubén, 2015. "Ranking Edges and Model Selection in High-Dimensional Graphs," DES - Working Papers. Statistics and Econometrics. WS ws1511, Universidad Carlos III de Madrid. Departamento de Estadística.
    21. Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.

    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:taf:jnlasa:v:112:y:2017:i:517:p:424-435. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.