IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v17y2024i8p346-d1453575.html

Econometric Analysis of SOFIX Index with GARCH Models

Author

Listed:
  • Plamen Petkov

    (Department of Statistics and Applied Mathematics, Tsenov Academy of Economics, 5250 Svishtov, Bulgaria)

  • Margarita Shopova

    (Department of Statistics and Applied Mathematics, Tsenov Academy of Economics, 5250 Svishtov, Bulgaria)

  • Tihomir Varbanov

    (Department of Statistics and Applied Mathematics, Tsenov Academy of Economics, 5250 Svishtov, Bulgaria)

  • Evgeni Ovchinnikov

    (Department of Statistics and Applied Mathematics, Tsenov Academy of Economics, 5250 Svishtov, Bulgaria)

  • Angelin Lalev

    (Department of Business Informatics, Tsenov Academy of Economics, 5250 Svishtov, Bulgaria)

Abstract

This paper investigates five different Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Condition-al Heteroscedacity (GARCH models (GARCH, exponential GARCH or EGARCH, integrated GARCH or IGARCH, Component GARCH or CGARCH and the Glosten-Jagannathan-Runkle GARCH or GJR-GARCH) along with six distributions (normal, Student’s t , GED and their skewed forms), which are used to estimate the price dynamics of the Bulgarian stock index SOFIX. We use the best model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data cover the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at analysing the SOFIX price and which distribution is most appropriate. The results, based on the BIC and AIC, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student’s t -distribution is preferred for modelling. From the results obtained, we can confirm that the CGARCH model specification supports a more appropriate description of SOFIX volatility than a simple GARCH model. We find that long-term shocks have a more persistent impact on volatility than the effect of short-term shocks. Furthermore, for the same magnitude, negative shocks to SOFIX prices have a more significant impact on volatility than positive shocks. According to the results, when predicting future values of SOFIX, it is necessary to include both a first-order autoregressive component and a first-order moving average in the mean equation. With the help of 5000 simulations, it is estimated that the chances of SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087.

Suggested Citation

  • Plamen Petkov & Margarita Shopova & Tihomir Varbanov & Evgeni Ovchinnikov & Angelin Lalev, 2024. "Econometric Analysis of SOFIX Index with GARCH Models," JRFM, MDPI, vol. 17(8), pages 1-30, August.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:8:p:346-:d:1453575
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/17/8/346/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/17/8/346/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vladimir Tsenkov, 2011. "Efficient-Market Hypothesis and the Global Financial Crises – on the Example of SOFIX, DJIA and DAX Indexes," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 3, pages 53-88.
    2. Josip ARNERIĆ & Blanka ŠKRABIĆ PERIĆ, 2018. "Panel GARCH Model with Cross-Sectional Dependence between CEE Emerging Markets in Trading Day Effects Analysis," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 71-84, December.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Mariana Petrova & Teodor Todorov, 2023. "Empirical Testing of Models of Autoregressive Conditional Heteroscedasticity Used for Prediction of the Volatility of Bulgarian Investment Funds," Risks, MDPI, vol. 11(11), pages 1-30, November.
    5. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    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. Krzysztof Ziółkowski & Paweł Wieczyński, 2026. "Enhancing financial time series forecasting: a comparative study of discrete wavelet transform and LSTM models for selected global indices," Quality & Quantity: International Journal of Methodology, Springer, vol. 60(1), pages 1995-2015, February.

    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. Leopoldo Catania & Stefano Grassi, 2017. "Modelling Crypto-Currencies Financial Time-Series," CEIS Research Paper 417, Tor Vergata University, CEIS, revised 11 Dec 2017.
    2. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    3. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    4. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    5. Dongming Zhu & John W. Galbraith, 2009. "Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution," CIRANO Working Papers 2009s-24, CIRANO.
    6. Ewing, Bradley T. & Malik, Farooq, 2017. "Modelling asymmetric volatility in oil prices under structural breaks," Energy Economics, Elsevier, vol. 63(C), pages 227-233.
    7. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, Enero-Abr.
    8. Benavides, Guillermo & Capistrán, Carlos, 2012. "Forecasting exchange rate volatility: The superior performance of conditional combinations of time series and option implied forecasts," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 627-639.
    9. Abadir, Karim M. & Luati, Alessandra & Paruolo, Paolo, 2023. "GARCH density and functional forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 470-483.
    10. Chiarella, Carl & He, Xue-Zhong & Zwinkels, Remco C.J., 2014. "Heterogeneous expectations in asset pricing: Empirical evidence from the S&P500," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 1-16.
    11. Alessandra Amendola & Christian Francq, 2009. "Concepts of and tools for Nonlinear Time-Series Modelling," Post-Print hal-05417886, HAL.
    12. Johannes W. Fedderke, 2020. "Is the Phillips curve framework still useful for understanding inflation dynamics in South Africa," Working Papers 10142, South African Reserve Bank.
    13. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    14. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    15. Catania, Leopoldo & Grassi, Stefano, 2022. "Forecasting cryptocurrency volatility," International Journal of Forecasting, Elsevier, vol. 38(3), pages 878-894.
    16. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521817707, Enero-Abr.
    17. Cristiana Tudor & Aura Girlovan & Gabriel Robert Saiu & Daniel Dumitru Guse, 2025. "Asymmetric Shocks and Pension Fund Volatility: A GARCH Approach with Macroeconomic Predictors to an Unexplored Emerging Market," Mathematics, MDPI, vol. 13(7), pages 1-29, March.
    18. Aharon, David Y. & Butt, Hassan Anjum & Jaffri, Ali & Nichols, Brian, 2023. "Asymmetric volatility in the cryptocurrency market: New evidence from models with structural breaks," International Review of Financial Analysis, Elsevier, vol. 87(C).
    19. Sera Şanlı & Mehmet Balcılar & Mehmet Özmen, 2025. "Predicting the volatility of Bitcoin returns based on kernel regression," Annals of Operations Research, Springer, vol. 352(3), pages 505-542, September.
    20. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2011. "Are realized volatility models good candidates for alternative Value at Risk prediction strategies?," MPRA Paper 30364, University Library of Munich, Germany.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jjrfmx:v:17:y:2024:i:8:p:346-:d:1453575. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.