Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes
Many authors have observed what is known as the Taylor property, namely that the time series dependencies of financial volatility as measured by the autocorrelation function of power-transformed absolute returns are stronger for absolute stock returns than for the squares. In this note, we devise a simple method for detecting the Taylor property at any lag in a class of GARCH(1, 1) models and fully characterize the relevant parameter space for several popular conditional distributions. It turns out that (i) very generally a first-order Taylor property implies the Taylor property at any lag, and (ii) the degree of conditional kurtosis is crucial for the appearance of the effect. This generalizes earlier findings in He and Teräsvirta [He, C., Teräsvirta, T., 1999. Properties of moments of a family of GARCH processes. Journal of Econometrics 92, 173-192] and Gonçalves etÂ al. [Gonçalves, E., Leite, J., Mendes-Lopes, N., 2009. A mathematical approach to detect the Taylor property in TARCH processes. Statistics and Probability Letters 79, 602-610] which focus on first-order autocorrelations and/or pure ARCH processes only. An application to the S&P500 index illustrates the results.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 79 (2009)
Issue (Month): 15 (August)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Helena Veiga, 2009. "Comment on "Financial Stylized Facts and the Taylor-Effect in Stochastic Volatility Models" by H. Veiga," Economics Bulletin, AccessEcon, vol. 29(4), pages 2730-2731.
- Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
- Esther Ruiz & Helena Veiga, 2006.
"Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch,"
Statistics and Econometrics Working Papers
ws066016, Universidad Carlos III, Departamento de Estadística y Econometría.
- Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
- Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
- repec:cup:cbooks:9780521779654 is not listed on IDEAS
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
- Helena Veiga, 2009. "Financial Stylized Facts and the Taylor-Effect in Stochastic Volatility Models," Economics Bulletin, AccessEcon, vol. 29(1), pages 265-276.
- Shiqing Ling & Michael McAleer, 2001.
"Stationarity and the Existence of Moments of a Family of GARCH Processes,"
ISER Discussion Paper
0535, Institute of Social and Economic Research, Osaka University.
- Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
- Granger, Clive W.J., 2005. "The past and future of empirical finance: some personal comments," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 35-40.
- Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998.
"Stylized facts of daily return series and the hidden Markov model,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
- Rydén, Tobias & Teräsvirta, Timo & Åsbrink, Stefan, 1996. "Stylized Facts of Daily Return Series and the Hidden Markov Model," SSE/EFI Working Paper Series in Economics and Finance 117, Stockholm School of Economics.
- Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
- 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.
- He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
- Fornari, Fabio & Mele, Antonio, 1994. "A stochastic variance model for absolute returns," Economics Letters, Elsevier, vol. 46(3), pages 211-214, November.
- repec:cup:cbooks:9780521770415 is not listed on IDEAS
- Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
- Alberto Mora-Galan & Ana Perez & Esther Ruiz, 2004. "Stochastic Volatility Models And The Taylor Effect," Statistics and Econometrics Working Papers ws046315, Universidad Carlos III, Departamento de Estadística y Econometría.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- Liu, Ji-Chun, 2006. "On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1323-1330, July.
- C. W. J. GRANGER & Zhuanxin DING, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annales d'Economie et de Statistique, ENSAE, issue 40, pages 67-91.
- Shaun A. Bond, 2006. "Asymmetry, Loss Aversion, and Forecasting," The Journal of Business, University of Chicago Press, vol. 79(4), pages 1809-1830, July.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:79:y:2009:i:15:p:1674-1683. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.