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

Hans Malmsten () and Timo Teräsvirta
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Hans Malmsten: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden

No 563, SSE/EFI Working Paper Series in Economics and Finance from 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.

Keywords: Autoregressive conditional heteroskedasticity; evaluation of volatility models; exponential GARCH; GARCH; modelling return series; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2004-08-25, Revised 2004-09-03
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

Published in European Journal of Pure and Applied Mathematics, 2010, pages 417-443.

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Persistent link: https://EconPapers.repec.org/RePEc:hhs:hastef:0563

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