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Stylized Facts of Financial Time Series and Three Popular Models of Volatility

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  • Malmsten, Hans

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

Properties of three well-known and frequently applied first-order models for modelling and forecasting volatility in financial series such as stock and exchange rate returns are considered. These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH and the Autoregressive Stochastic Volatility model. The focus is on finding out how well these models are able to reproduce characteristic features of such series, also called stylized facts. These include high kurtosis and a rather low-starting and slowly decaying autocorrelation function of the squared or absolute-valued observations. Another stylized fact is that the autocorrelations of absolute-valued returns raised to a positive power are maximized when this power equals unity. A number of results for moments of the three models are given as well as the autocorrelation function of squared observations or, when available, the autocorrelation function of the absolute-valued observations raised to a positive power. These results make it possible to consider kurtosis-autocorrelation combinations that can be reproduced with these models and compare them with ones that have been estimated from financial time series. The ability of the models to reproduce the stylized fact that the autocorrelations of powers of absolute-valued observations are maximized when the power equals one is discussed as well. Finally, it is pointed out that none of these basic models can generate realizations with a skewed marginal distribution. Not unexpectedly, a conclusion that emerges from these considerations, largely based on results on the moment structure of these models, is that none of the models dominates the others when it comes to reproducing stylized facts in typical financial time series.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 563.

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Length: 42 pages
Date of creation: 25 Aug 2004
Date of revision: 03 Sep 2004
Publication status: Published in European Journal of Pure and Applied Mathematics, 2010, pages 417-443.
Handle: RePEc:hhs:hastef:0563

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Keywords: Autoregressive conditional heteroskedasticity; evaluation of volatility models; exponential GARCH; GARCH; modelling return series; stochastic volatility;

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Cited by:
  1. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Modelling and Forecasting Noisy Realized Volatility," KIER Working Papers, Kyoto University, Institute of Economic Research 758, Kyoto University, Institute of Economic Research.
  2. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, Elsevier, vol. 147(1), pages 104-119, November.
  3. María García Centeno & Román Mínguez Salido, 2009. "Estimation of Asymmetric Stochastic Volatility Models for Stock-Exchange Index Returns," International Advances in Economic Research, Springer, Springer, vol. 15(1), pages 71-87, February.
  4. Alberto Mora-Galan & Ana Perez & Esther Ruiz, 2004. "Stochastic Volatility Models And The Taylor Effect," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws046315, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Kovačić, Zlatko, 2007. "Forecasting volatility: Evidence from the Macedonian stock exchange," MPRA Paper 5319, University Library of Munich, Germany.
  6. Oleg Korenok & Stanislav Radchenko, 2005. "The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications," Working Papers, VCU School of Business, Department of Economics 0505, VCU School of Business, Department of Economics.
  7. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance, Stockholm School of Economics 646, Stockholm School of Economics.
  8. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
  9. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(15), pages 1674-1683, August.

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