Stylized facts of return series, robust estimates and three popular models of volatility

Abstract

Financial return series of sufficiently high frequency display stylized facts such as volatility clustering, high kurtosis, low starting and slow-decaying autocorrelation function of squared returns and the so-called Taylor effect. In order to evaluate the capacity of volatility models to reproduce these facts, we apply both standard and robust measures of kurtosis and autocorrelation of squares to first-order Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Exponential GARCH (EGARCH) and Autoregressive Stochastic Volaticity (ARSV) models. Robust measures provide a fresh view of stylized facts, which is useful because many financial time series can be viewed as being contaminated with outliers.

Acknowledgements

This work was supported by the Danish National Research Foundation and Stockholm School of Economics. Material from this article has been presented at ‘Volatility Day’ Workshop at Stockholm School of Economics, November 2006, Workshop on Econometrics and Computational Economics II/2006, Helsinki, December 2006, Zeuthen Workshop on Financial Econometrics, Copenhagen, December 2006 and the Fourth Nordic Econometric Meeting, Tartu, May 2007. We thank participants for their comments. We also wish to thank Changli He and Pentti Saikkonen for useful suggestions. T. Teräsvirta bears full responsibility for any errors and shortcomings in this work.

Notes

^†This article is dedicated to Clive Granger and to my graduate student and co-author Zhenfang Zhao who died after a brief illness after the work had been completed. I miss them both.

¹The working paper version of this article was completed in 2003.

²That happens in this series but it is not a frequent event.

³It is straightforward to produce confidence regions at other levels. For typical graphs, see Malmsten and Teräsvirta (2010).

Additional information

Notes on contributors

Zhenfang Zhao†

†This article is dedicated to Clive Granger and to my graduate student and co-author Zhenfang Zhao who died after a brief illness after the work had been completed. I miss them both.