IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i5p602-610.html
   My bibliography  Save this article

A mathematical approach to detect the Taylor property in TARCH processes

Author

Listed:
  • Gonçalves, Esmeralda
  • Leite, Joana
  • Mendes-Lopes, Nazaré

Abstract

We analyze the presence of the Taylor property in a well-known class of models for financial time series, the threshold ARCH (TARCH) model. This property is the theoretical counterpart of the stylized fact known as Taylor effect, detected in several empirical studies which have shown that the autocorrelations of the absolute returns are larger than those of the squared returns. We establish that the Taylor property is present for some parameterizations of the first order TARCH model. As this fact is strongly dependent on the distribution of the generating white noise, we analyze and compare, for several distributions of that process, the sets of parameterizations of the model presenting the Taylor property. Finally, a simulation study strongly suggests that TARCH models are considerably more likely to capture the Taylor effect than ARCH ones.

Suggested Citation

  • Gonçalves, Esmeralda & Leite, Joana & Mendes-Lopes, Nazaré, 2009. "A mathematical approach to detect the Taylor property in TARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 602-610, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:602-610
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00472-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
    2. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    3. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    4. Mora Galán, Alberto & Pérez, Ana & Ruiz Ortega, Esther, 2004. "Stochastic volatility models and the Taylor effect," DES - Working Papers. Statistics and Econometrics. WS ws046315, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. repec:adr:anecst:y:1995:i:40:p:04 is not listed on IDEAS
    6. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    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. Gonçalves, E. & Mendes-Lopes, N., 2010. "On the structure of generalized threshold arch processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 573-580, April.
    2. Ruiz Esther & Pérez Ana, 2012. "Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-33, September.
    3. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
    4. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.

    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. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    2. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
    3. Marcelo Cunha Medeiros & Alvaro Veiga, 2004. "Modelling multiple regimes in financial volatility with a flexible coefficient GARCH model," Textos para discussão 486, Department of Economics PUC-Rio (Brazil).
    4. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    5. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    6. Carnero, María Ángeles & Peña, Daniel & Ruiz Ortega, Esther, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," Post-Print hal-01943883, HAL.
    8. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
    9. repec:hal:wpaper:hal-01943883 is not listed on IDEAS
    10. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    11. Alin Sima, 2008. "Stylized Facts and Discrete Stochastic Volatility Models," Advances in Economic and Financial Research - DOFIN Working Paper Series 10, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    12. Výrost, Tomáš & Baumöhl, Eduard, 2009. "Asymmetric GARCH and the financial crisis: a preliminary study," MPRA Paper 27939, University Library of Munich, Germany.
    13. Tzu-Yi Yang & Yu-Tai Yang, 2015. "A Study on the Asymmetry of the News Aspect of the Stock Market: Evidence from Three Institutional Investors in the Taiwan Stock Market," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 62(3), pages 361-383, June.
    14. Josu Arteche, 2012. "Standard and seasonal long memory in volatility: an application to Spanish inflation," Empirical Economics, Springer, vol. 42(3), pages 693-712, June.
    15. Francesco Audrino & Fabio Trojani, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369, April.
    16. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    17. 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).
    18. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.
    19. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
    20. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August.
    21. Rustam Ibragimov & Rasmus Pedersen & Anton Skrobotov, 2020. "New Approaches to Robust Inference on Market (Non-)Efficiency, Volatility Clustering and Nonlinear Dependence," Papers 2006.01212, arXiv.org, revised Nov 2023.

    More about this item

    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:eee:stapro:v:79:y:2009:i:5:p:602-610. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.