Breaks and outliers when modelling the volatility of the U.S. stock market

ABSTRACT

This study analyses volatility persistence of the U.S. stock market, after taking into account the role of breaks and outliers. By employing a wavelet-based algorithm, it identifies several outliers which are comfortably associated with major events such as the ‘Black Monday’ and the Asian crisis. There is also evidence of clustering of breaks and a substantial variation in the properties of the identified segments.

KEYWORDS:

• Stock returns
• outliers
• structural breaks
• GARCH

JEL CLASSIFICATION:

• C12
• C22
• C59
• G10
• G15

Acknowledgment

The author acknowledges financial support from the University of Patras (Caratheodory Research Grant C.909) and would like to thank Michail Karoglou and an anonymous referee for valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ The procedure allows for only one detected outlier at a time, which means that when an outlier is detected then the series is corrected and the adjusted series is used for the detection of a new outlier.

² The algorithm can be extended to other error distributions, such as the Generalized Error Distribution.

³ Following De Pooter and Van Dijk (2004), we impose a minimum distance between adjacent breaks of 3 business months to prevent breaks from being identified unrealistically close.

⁴ The autoregressive parameter is included in the conditional mean, if series show evidence of autocorrelation indicated by the autocorrelation and partial autocorrelation functions.

⁵ A threshold value of $k_1^{0.05}=4.3521$ computed from 20,000 Monte Carlo replications of size $n=7700$ is used.

⁶ In the case of a volatility model with the errors following a Student’s t-distribution, no outliers are detected, in accordance with the findings of Grané and Veiga (2010).

⁷ On 19 October 1987, the fall of the DJIA is recorded as the largest one-day percentage decline from 1928 to 2010 (Charles and Darné, 2014).

⁸ Results for the remaining indices are available upon request.

⁹ Due to space limitations, we do not report the results from the tests for the equality of mean and variance of contiguous segments; however, the relevant results are available upon request.

¹⁰ This finding is in accordance with the existing literature, see for instance Charles and Darne (2006), Carnero et al. (2007, 2012) and Franses and Ghijsels (1999).

¹¹ The findings are similar to other studies, see for example, Aggarwal, Inclán, and Leal (1999) Ewing and Malik (2010), and Wang and Moore (2009).

¹² Overall, our results are in accordance with Lamoureux and Lastrapes (1990), who argue that standard GARCH model overestimates the persistence in volatility since relevant sudden changes in variance are ignored.

¹³ Similar results for subsample GARCH estimates have been employed in Rapach et al. (2008), McMillan and Wohar (2011) and Vivian and Wohar (2012) among others.

Additional information

Funding

The author acknowledges funding from the University of Patras [Caratheodory Research Grant C.909].