Testing asymmetry in financial time series

Abstract

This paper examines the problem of evaluating the presence of asymmetry in the marginal distribution of financial returns by means of a suitable statistical test. After a brief description of existing tests, a bootstrap procedure is proposed. A Monte Carlo study showed that this test works properly and that, in terms of power, it is competitive with existing tests. An application to real financial time series is also presented.

Keywords:

• Skewness
• Symmetry test
• Financial returns
• Bootstrap

Acknowledgements

I would like to thank Adelchi Azzalini, Silvano Bordignon, Nunzio Cappuccio and Amado Peiró for their help and suggestions and two anonymous referees for useful comments. Thanks are due to Serena Ng who provided the software for the Bai and Ng (2005) test. Financial support from the Italian MIUR is also gratefully acknowledged.

Notes

†Note that here we do not refer to the asymmetrical effects that negative and positive returns may have on volatility, but to the symmetry of the marginal distribution of returns.

†This implies that, critical values depend on what data generating process is used to determine the distribution under the null hypothesis. A possible way to face this problem, but not pursued here, is described by Beran (1988).