IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p945-d542075.html
   My bibliography  Save this article

An Analytical EM Algorithm for Sub-Gaussian Vectors

Author

Listed:
  • Audrius Kabašinskas

    (Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Leonidas Sakalauskas

    (Šiauliai Academy, Vilnius University, 76352 Šiauliai, Lithuania)

  • Ingrida Vaičiulytė

    (Faculty of Business and Technologies, Šiauliai State College, 76241 Šiauliai, Lithuania)

Abstract

The area in which a multivariate α -stable distribution could be applied is vast; however, a lack of parameter estimation methods and theoretical limitations diminish its potential. Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α -stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate α -stable random variables. Our numerical results show that the convergence of the proposed algorithm is much faster than that of existing algorithms. Moreover, the likelihood ratio (goodness-of-fit) test for a multivariate α -stable distribution was implemented. Empirical examples with simulated and real world (stocks, AIS and cryptocurrencies) data showed that the likelihood ratio test can be useful for assessing goodness-of-fit.

Suggested Citation

  • Audrius Kabašinskas & Leonidas Sakalauskas & Ingrida Vaičiulytė, 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:945-:d:542075
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/945/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/945/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael McAssey, 2013. "An empirical goodness-of-fit test for multivariate distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 1120-1131.
    2. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    3. Leonidas Sakalauskas, 2010. "On the Empirical Bayesian Approach for the Poisson-Gaussian Model," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 247-259, June.
    4. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    5. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    6. Ravishanker, Nalini & Qiou, Zuqiang, 1999. "Monte Carlo EM estimation for multivariate stable distributions," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 335-340, December.
    7. Noureddine Kouaissah & Sergio Ortobelli lozza, 2020. "Multivariate Stochastic Dominance: A Parametric Approach," Economics Bulletin, AccessEcon, vol. 40(2), pages 1380-1387.
    8. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    9. Press, S. J., 1972. "Multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 444-462, December.
    10. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, 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. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    2. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    3. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    4. Torri, Gabriele & Giacometti, Rosella & Paterlini, Sandra, 2018. "Robust and sparse banking network estimation," European Journal of Operational Research, Elsevier, vol. 270(1), pages 51-65.
    5. Bielak, Łukasz & Grzesiek, Aleksandra & Janczura, Joanna & Wyłomańska, Agnieszka, 2021. "Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling," Resources Policy, Elsevier, vol. 74(C).
    6. Simos G. Meintanis, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 898-902, December.
    7. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    8. Yiying Cheng & Yaozhong Hu & Hongwei Long, 2020. "Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 53-81, April.
    9. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    10. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    11. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    12. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    13. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    14. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    15. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    16. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    17. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    18. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    19. Jie Shi & Arno P. J. M. Siebes & Siamak Mehrkanoon, 2023. "TransCORALNet: A Two-Stream Transformer CORAL Networks for Supply Chain Credit Assessment Cold Start," Papers 2311.18749, arXiv.org.
    20. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.

    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:gam:jmathe:v:9:y:2021:i:9:p:945-:d:542075. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.