IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3849-d945153.html
   My bibliography  Save this article

Asymptotic Properties and Application of GSB Process: A Case Study of the COVID-19 Dynamics in Serbia

Author

Listed:
  • Mihailo Jovanović

    (The Office for Information Technologies and eGovernment, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Vladica Stojanović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Kristijan Kuk

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Brankica Popović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Petar Čisar

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

Abstract

This paper describes one of the non-linear (and non-stationary) stochastic models, the GSB (Gaussian, or Generalized, Split-BREAK) process, which is used in the analysis of time series with pronounced and accentuated fluctuations. In the beginning, the stochastic structure of the GSB process and its important distributional and asymptotic properties are given. To that end, a method based on characteristic functions (CFs) was used. Various procedures for the estimation of model parameters, asymptotic properties, and numerical simulations of the obtained estimators are also investigated. Finally, as an illustration of the practical application of the GSB process, an analysis is presented of the dynamics and stochastic distribution of the infected and immunized population in relation to the disease COVID-19 in the territory of the Republic of Serbia.

Suggested Citation

  • Mihailo Jovanović & Vladica Stojanović & Kristijan Kuk & Brankica Popović & Petar Čisar, 2022. "Asymptotic Properties and Application of GSB Process: A Case Study of the COVID-19 Dynamics in Serbia," Mathematics, MDPI, vol. 10(20), pages 1-28, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3849-:d:945153
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3849/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3849/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
    2. Dendramis, Yiannis & Kapetanios, George & Tzavalis, Elias, 2014. "Level shifts in stock returns driven by large shocks," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 41-51.
    3. Dendramis, Yiannis & Kapetanios, George & Tzavalis, Elias, 2015. "Shifts in volatility driven by large stock market shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 130-147.
    4. Gonzalo, Jesus & Martinez, Oscar, 2006. "Large shocks vs. small shocks. (Or does size matter? May be so.)," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 311-347.
    5. Samiran Ghosh & Vitaly Volpert & Malay Banerjee, 2022. "An Epidemic Model with Time Delay Determined by the Disease Duration," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    6. Kapetanios, G. & Tzavalis, E., 2010. "Modeling structural breaks in economic relationships using large shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 417-436, March.
    7. A. J. Lawrance & P. A. W. Lewis, 1992. "Reversed Residuals In Autoregressive Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 253-266, May.
    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. Alexander N. Tikhomirov & Vladimir V. Ulyanov, 2023. "On the Special Issue “Limit Theorems of Probability Theory”," Mathematics, MDPI, vol. 11(17), pages 1-4, August.

    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. Dendramis, Yiannis & Kapetanios, George & Tzavalis, Elias, 2015. "Shifts in volatility driven by large stock market shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 130-147.
    2. 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.
    3. Y. Dendramis & G. Kapetanios & M. Marcellino, 2020. "A similarity‐based approach for macroeconomic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 801-827, June.
    4. Dendramis, Yiannis & Kapetanios, George & Tzavalis, Elias, 2014. "Level shifts in stock returns driven by large shocks," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 41-51.
    5. J. Cuñado & L. Gil-Alana & F. Gracia, 2009. "US stock market volatility persistence: evidence before and after the burst of the IT bubble," Review of Quantitative Finance and Accounting, Springer, vol. 33(3), pages 233-252, October.
    6. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.
    7. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    8. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    9. Kapetanios, G. & Tzavalis, E., 2010. "Modeling structural breaks in economic relationships using large shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 417-436, March.
    10. Guglielmo Maria Caporale & Hector Carcel & Luis A. Gil-Alana, 2015. "Modelling African inflation rates: nonlinear deterministic terms and long-range dependence," Applied Economics Letters, Taylor & Francis Journals, vol. 22(5), pages 421-424, March.
    11. Monticini, Andrea & Ravazzolo, Francesco, 2014. "Forecasting the intraday market price of money," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 304-315.
    12. Dominique Guegan & Philippe de Peretti, 2011. "Tests of structural changes in conditional distributions with unknown changepoints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00611932, HAL.
    13. Chen, Haiqiang & Choi, Paul Moon Sub & Hong, Yongmiao, 2013. "How smooth is price discovery? Evidence from cross-listed stock trading," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 668-699.
    14. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
    16. Ioannidis, Christos & Ka, Kook, 2018. "The impact of oil price shocks on the term structure of interest rates," Energy Economics, Elsevier, vol. 72(C), pages 601-620.
    17. Eklund, Jana & Kapetanios, George & Price, Simon, 2010. "Forecasting in the presence of recent structural change," Bank of England working papers 406, Bank of England.
    18. Hyung, Namwon & Franses, Philip Hans & Penm, Jack, 2006. "Structural breaks and long memory in US inflation rates: Do they matter for forecasting?," Research in International Business and Finance, Elsevier, vol. 20(1), pages 95-110, March.
    19. George Kapetanios & Tony Yates, 2014. "Evolving UK and US macroeconomic dynamics through the lens of a model of deterministic structural change," Empirical Economics, Springer, vol. 47(1), pages 305-345, August.
    20. Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.

    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:10:y:2022:i:20:p:3849-:d:945153. 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.