IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42548.html
   My bibliography  Save this paper

Un modelo GARCH con asimetría condicional autorregresiva para modelar series de tiempo: Una aplicación para el Indice de Precios y Cotizaciones
[A GARCH model with autorregresive conditional asymmetry to model time-series: An application to the returns of the Mexican Stock Market Index]

Author

Listed:
  • Durán-Vázquez, Rocio
  • Lorenzo-Valdes, Arturo
  • Ruiz-Porras, Antonio

Abstract

We develop a GARCH model with autoregressive conditional asymmetry to describe time-series. This means that, in addition to the conditional mean and variance, we assume that the skewness describes the behavior of the time-series. Analytically, we use the methodology proposed by Fernández and Steel (1998) to define the behavior of the innovations of the model. We use the approach developed by Brooks, et. al., (2005), to build it. Moreover, we show its usefulness by modeling the daily returns of the Mexican Stock Market Index (IPC) during the period between January 3rd, 2008 and September 29th, 2009.

Suggested Citation

  • Durán-Vázquez, Rocio & Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2012. "Un modelo GARCH con asimetría condicional autorregresiva para modelar series de tiempo: Una aplicación para el Indice de Precios y Cotizaciones [A GARCH model with autorregresive conditional asymme," MPRA Paper 42548, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42548
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42548/1/MPRA_paper_42548.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2001. "Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices," Journal of Financial Economics, Elsevier, vol. 61(3), pages 345-381, September.
    2. Bollerslev, Tim & Russell, Jeffrey & Watson, Mark (ed.), 2010. "Volatility and Time Series Econometrics: Essays in Honor of Robert Engle," OUP Catalogue, Oxford University Press, number 9780199549498.
    3. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    4. Duran-Vazquez, Rocio & Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2011. "Valuation of Latin-American stock prices with alternative versions of the Ohlson model: An investigation of cointegration relationships with time-series and panel-data," MPRA Paper 31354, University Library of Munich, Germany.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Doaa Akl Ahmed, 2011. "Modelling the Density of Inflation Using Autoregressive Conditional Heteroscedasticity, Skewness, and Kurtosis Models," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 1-28, November.
    7. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    8. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    9. Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2011. "Modelación de los rendimientos bursátiles mexicanos mediante los modelos TGARCH y EGARCH: Un estudio econométrico para 30 acciones y el Índice de Precios y Cotizaciones [Modeling Mexican stock retu," MPRA Paper 36872, University Library of Munich, Germany.
    10. Manganelli, Simone & White, Halbert & Kim, Tae-Hwan, 2008. "Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR," Working Paper Series 957, European Central Bank.
    11. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 399-421.
    12. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    13. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    14. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    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. Duran-Vazquez, Rocio & Lorenzo-Valdes, Arturo & Ruiz-Porras, Antonio, 2013. "Un modelo GARCH con asimetria condicional autorregresiva para modelar series de tiempo: Una aplicacion para los rendimientos del Indice de Precios y Cotizaciones de la BMV [A GARCH model with autor," MPRA Paper 46328, University Library of Munich, Germany.
    2. Arturo Lorenzo Valdés & Antonio Ruiz Porras, 2014. "Un modelo Tgarch con una distribución t de student asimétrica y las hipótesis de racionalidad de los inversionistas bursátiles en Latinoamérica," Archivos Revista Economía y Política., Facultad de Ciencias Económicas y Administrativas, Universidad de Cuenca., vol. 19, pages 66-97, Enero.
    3. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    4. Eric Jondeau & Michael Rockinger, 2005. "Conditional Asset Allocation under Non-Normality: How Costly is the Mean-Variance Criterion?," FAME Research Paper Series rp132, International Center for Financial Asset Management and Engineering.
    5. Yang (Greg) Hou & Mark Holmes, 2020. "Do higher order moments of return distribution provide better decisions in minimum-variance hedging? Evidence from US stock index futures," Australian Journal of Management, Australian School of Business, vol. 45(2), pages 240-265, May.
    6. Hou, Yang (Greg) & Li, Steven, 2020. "Volatility and skewness spillover between stock index and stock index futures markets during a crash period: New evidence from China," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 166-188.
    7. Hashmi, Aamir R. & Tay, Anthony S., 2007. "Global regional sources of risk in equity markets: Evidence from factor models with time-varying conditional skewness," Journal of International Money and Finance, Elsevier, vol. 26(3), pages 430-453, April.
    8. Shum, Wai Yan, 2020. "Modelling conditional skewness: Heterogeneous beliefs, short sale restrictions and market declines," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    9. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    10. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    11. Lai, Jing-yi, 2012. "Shock-dependent conditional skewness in international aggregate stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(1), pages 72-83.
    12. Hou, Yang & Holmes, Mark, 2017. "On the effects of static and autoregressive conditional higher order moments on dynamic optimal hedging," MPRA Paper 82000, University Library of Munich, Germany.
    13. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2017. "The kidnapping of Europe: High-order moments' transmission between developed and emerging markets," Emerging Markets Review, Elsevier, vol. 31(C), pages 96-115.
    14. Hutson, Elaine & Kearney, Colm & Lynch, Margaret, 2008. "Volume and skewness in international equity markets," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1255-1268, July.
    15. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    16. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
    17. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    18. Ryo Kinoshita, 2015. "Asset allocation under higher moments with the GARCH filter," Empirical Economics, Springer, vol. 49(1), pages 235-254, August.
    19. repec:hum:wpaper:sfb649dp2016-001 is not listed on IDEAS
    20. Sylvia J. Soltyk & Felix Chan, 2023. "Modeling time‐varying higher‐order conditional moments: A survey," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 33-57, February.
    21. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2016. "Portfolio selection with a systematic skewness constraint," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 393-405.

    More about this item

    Keywords

    Conditional Asymmetry; GARCH; Skewness; Stock Market Returns; Mexico;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:42548. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.