Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes
AbstractMany 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 79 (2009)
Issue (Month): 15 (August)
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- He, Changli & Teräsvirta, Timo, 1997.
"Properties of Moments of a Family of GARCH Processes,"
Working Paper Series in Economics and Finance
198, Stockholm School of Economics.
- 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.
- 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.
- Shaun A. Bond, 2006. "Asymmetry, Loss Aversion, and Forecasting," The Journal of Business, University of Chicago Press, vol. 79(4), pages 1809-1830, July.
- 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.
- 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.
- 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.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- 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.
- 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," Working Paper Series in Economics and Finance 117, Stockholm School of Economics.
- 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.
- Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Franses,Philip Hans & Dijk,Dick van, 2000.
"Non-Linear Time Series Models in Empirical Finance,"
Cambridge University Press, number 9780521779654.
- Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
- Helena Veiga, 2009. "Financial Stylized Facts and the Taylor-Effect in Stochastic Volatility Models," Economics Bulletin, AccessEcon, vol. 29(1), pages 265-276.
- 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.
- Fornari, Fabio & Mele, Antonio, 1994. "A stochastic variance model for absolute returns," Economics Letters, Elsevier, vol. 46(3), pages 211-214, November.
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