IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v76y2024i5d10.1007_s10463-024-00902-z.html
   My bibliography  Save this article

A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance

Author

Listed:
  • Žikica Lukić

    (University of Belgrade)

  • Bojana Milošević

    (University of Belgrade)

Abstract

This paper introduces a novel two-sample test for a broad class of orthogonally invariant positive definite symmetric matrix distributions. Our test is the first of its kind, and we derive its asymptotic distribution. To estimate the test power, we use a warp-speed bootstrap method and consider the most common matrix distributions. We provide several real data examples, including the data for main cryptocurrencies and stock data of major US companies. The real data examples demonstrate the applicability of our test in the context closely related to algorithmic trading. The popularity of matrix distributions in many applications and the need for such a test in the literature are reconciled by our findings.

Suggested Citation

  • Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:5:d:10.1007_s10463-024-00902-z
    DOI: 10.1007/s10463-024-00902-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-024-00902-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-024-00902-z?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. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2019. "Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 419-435, July.
    2. Jinan Liu & Apostolos Serletis, 2019. "Volatility in the Cryptocurrency Market," Open Economies Review, Springer, vol. 30(4), pages 779-811, September.
    3. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    4. Anoop S Kumar & Taufeeq Ajaz, 2019. "Co-movement in crypto-currency markets: evidences from wavelet analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 5(1), pages 1-17, December.
    5. Jinan Liu & Apostolos Serletis, 2019. "Volatility in the Cryptocurrency Market," Open Economies Review, Springer, vol. 30(4), pages 779-811, September.
    6. Gustav Alfelt & Taras Bodnar & Joanna Tyrcha, 2020. "Goodness-of-fit tests for centralized Wishart processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(20), pages 5060-5090, October.
    7. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    8. Ouimet, Frédéric, 2022. "A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. Tomarchio, Salvatore D. & Punzo, Antonio & Bagnato, Luca, 2020. "Two new matrix-variate distributions with application in model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    10. Simos Meintanis & George Iliopoulos, 2003. "Tests of fit for the Rayleigh distribution based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 137-151, March.
    11. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    12. Kaminski, Kathryn M. & Lo, Andrew W., 2014. "When do stop-loss rules stop losses?," Journal of Financial Markets, Elsevier, vol. 18(C), pages 234-254.
    13. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    14. Jeffrey Chu & Saralees Nadarajah & Stephen Chan, 2015. "Statistical Analysis of the Exchange Rate of Bitcoin," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-27, July.
    15. Fruehwirt, Wolfgang & Hochfilzer, Leonhard & Weydemann, Leonard & Roberts, Stephen, 2021. "Cumulation, crash, coherency: A cryptocurrency bubble wavelet analysis," Finance Research Letters, Elsevier, vol. 40(C).
    16. Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    17. Norbert Henze & Bernhard Klar, 2002. "Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 425-444, June.
    18. Lingzhe Guo & Reza Modarres, 2020. "Testing the equality of matrix distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 289-307, June.
    19. Min Shu & Ruiqiang Song & Wei Zhu, 2021. "The 2021 Bitcoin Bubbles and Crashes—Detection and Classification," Stats, MDPI, vol. 4(4), pages 1-21, November.
    20. Elena Hadjicosta & Donald Richards, 2020. "Integral transform methods in goodness-of-fit testing, II: the Wishart distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1317-1370, December.
    21. Elena Hadjicosta & Donald Richards, 2020. "Integral transform methods in goodness-of-fit testing, I: the gamma distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 733-777, October.
    22. Shanshan Ding & R. Dennis Cook, 2018. "Matrix variate regressions and envelope models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 387-408, March.
    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. Onur Özdemir, 2022. "Cue the volatility spillover in the cryptocurrency markets during the COVID-19 pandemic: evidence from DCC-GARCH and wavelet analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-38, December.
    2. Hwang, Yoontae & Park, Junpyo & Lee, Yongjae & Lim, Dong-Young, 2023. "Stop-loss adjusted labels for machine learning-based trading of risky assets," Finance Research Letters, Elsevier, vol. 58(PA).
    3. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    4. B M, Lithin & chakraborty, Suman & iyer, Vishwanathan & M N, Nikhil & ledwani, Sanket, 2022. "Modeling asymmetric sovereign bond yield volatility with univariate GARCH models: Evidence from India," MPRA Paper 117067, University Library of Munich, Germany, revised 05 Jan 2023.
    5. Vasu Kalariya & Pushpendra Parmar & Patel Jay & Sudeep Tanwar & Maria Simona Raboaca & Fayez Alqahtani & Amr Tolba & Bogdan-Constantin Neagu, 2022. "Stochastic Neural Networks-Based Algorithmic Trading for the Cryptocurrency Market," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    6. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    7. Silky Vigg Kushwah & Shab Hundal & Payal Goel, 2024. "Unveiling Interconnectedness and Volatility Transmission: A Novel GARCH Analysis of Leading Global Cryptocurrencies," International Journal of Economics and Financial Issues, Econjournals, vol. 14(3), pages 132-139, May.
    8. Fung, Kennard & Jeong, Jiin & Pereira, Javier, 2022. "More to cryptos than bitcoin: A GARCH modelling of heterogeneous cryptocurrencies," Finance Research Letters, Elsevier, vol. 47(PA).
    9. Jinan Liu & Sajjadur Rahman & Apostolos Serletis, 2021. "Cryptocurrency shocks," Manchester School, University of Manchester, vol. 89(2), pages 190-202, March.
    10. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," 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. 17(2), pages 323-345, June.
    11. Liu, Jinan & Valcarcel, Victor J., 2024. "Hedging inflation expectations in the cryptocurrency futures market," Journal of Financial Stability, Elsevier, vol. 70(C).
    12. Ivanovski, Kris & Hailemariam, Abebe, 2023. "Forecasting the stock-cryptocurrency relationship: Evidence from a dynamic GAS model," International Review of Economics & Finance, Elsevier, vol. 86(C), pages 97-111.
    13. Novi Maryaningsih & Suahasil Nazara & Febrio N. Kacaribu & Solikin M. Juhro, 2022. "Central Bank Digital Currency: What Factors Determine Its Adoption?," Bulletin of Monetary Economics and Banking, Bank Indonesia, vol. 25(1), pages 1-24, June.
    14. Jens Klose, 2022. "Comparing cryptocurrencies and gold - a system-GARCH-approach," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(4), pages 653-679, December.
    15. E. Bothma & J. S. Allison & I. J. H. Visagie, 2022. "New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring," Computational Statistics, Springer, vol. 37(4), pages 1751-1770, September.
    16. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    17. Qiao, Xingzhi & Zhu, Huiming & Hau, Liya, 2020. "Time-frequency co-movement of cryptocurrency return and volatility: Evidence from wavelet coherence analysis," International Review of Financial Analysis, Elsevier, vol. 71(C).
    18. Apostolos Ampountolas, 2022. "Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models," IJFS, MDPI, vol. 10(3), pages 1-22, July.
    19. De Pace, Pierangelo & Rao, Jayant, 2023. "Comovement and instability in cryptocurrency markets," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 173-200.
    20. Aiman Hairudin & Azhar Mohamad, 2024. "The isotropy of cryptocurrency volatility," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(3), pages 3779-3810, July.

    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:spr:aistmt:v:76:y:2024:i:5:d:10.1007_s10463-024-00902-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.