On the detection of extreme movements and persistent behaviour in Mediterranean stock markets: a wavelet-based approach

Abstract

We combine the global Hurst exponent and Morlet wavelet multi-resolution analysis (MRA) to investigate the dynamic behaviour of six selected stock markets in the Mediterranean region. Specifically, we employ the resonance coefficients and their power spectra to identify potential extreme movements and long-term dependence in stock returns. Using weekly data for the period 2005 to 2010, our results reveal that the wavelet MRA is able to reconstruct the effects of major extreme shocks on stock returns of studied markets, such as the Asian financial crisis, the 9/11 terrorist attacks and the 2007–2009 financial crisis. Moreover, the wavelet-based global Hurst exponent indicates the presence of long-term dependencies in stock returns of all the considered markets, except for France where the anti-persistent behaviour is detected. Overall, our findings are useful to assess the stock market efficiency and provide new insights into stock market dynamics over different time scales.

Keywords:

• persistence
• Mediterranean markets
• wavelet analysis
• Hurst exponent
• return behaviour

JEL Classifications:

• G15
• C14
• C58

Acknowledgements

The authors are grateful to the editor and an anonymous referee for their helpful comments.

Funding

C. Aloui would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project [RGP-VPP-211].

Notes

¹ For instance, only two studies have focused on the persistent behaviour of Latin American and Chinese stock markets (Kyaw et al., 2006, Los and Yu, 2008).

² As of November 2013, both S&P’s Morgan Stanley Capital International (MSCI) include Egypt and Turkey in their respective lists of emerging markets, while Tunisia is identified as a frontier emerging market which is investable, but has lower market capitalization and liquidity than emerging and developed markets.

³ Studies such as Gallegati (2005), Basdas (2012) and Graham et al. (2013) have shown from the wavelet analysis that MENA markets are only partially integrated at both the regional and global levels.

⁴ Banerjee and Urga (2005) provided an excellent literature overview in relation to modelling structural breaks, long memory and stock market volatility.

⁵ Grech and Mazur (2004) and Cajueiro and Tabak (2004) use a time-varying Hurst’s exponent to detect long-term autocorrelations in financial time series.

⁶ See Los (2003) for more technical details regarding the Morlet wavelet.

⁷ We also produce the quantile–quantile (QQ) plots of weekly return series and the results are consistent with the Jarque–Bera test for normality. For concision purpose, they are not displayed here, but can be made available upon request to the corresponding author.

⁸ The authors are particularly grateful to an anonymous referee for suggesting this preliminary investigation.

⁹ A Morlet-6 wavelet is advantageous in that it can precisely capture a nonsmooth asymmetric distribution by means of six nonvanishing moments (Kyaw et al., 2006). By contrast, a smooth and symmetric normal distribution has only two unique nonvanishing moments.

¹⁰ In the print version of this article, the red regions correspond to the darkest shading. For a better visualization of the graphs, please refer to the online version.

¹¹ We are grateful to an anonymous reviewer for this interesting suggestion.

¹² Jagric et al. (2005) and Cajueiro and Tabak (2008) use the traditional rescaled range and rescaled variance methods to investigate long-term dependence for a large sample of emerging and developed stock markets, and also provide evidence that emerging market returns exhibit stronger long-range dependence than developed market returns.