Superstitious seasonality in precious metals markets? Evidence from GARCH models with time-varying skewness and kurtosis

Abstract

In this article, we analyse whether the Friday the 13th effect documented by Kolb and Rodriguez (1987) can be observed in precious metals markets. Specifically, we use dummy-augmented GARCH models to investigate the impact of this specific calendar day on the conditional means of gold, silver, palladium and platinum returns. The specification of the GARCH model follows a flexible class recently proposed by León et al. (2005) that incorporates time-varying skewness and kurtosis by applying a Gram–Charlier series expansion of the normal density function. Our results for the period from July 1996 to August 2013 provide three important insights. First, there is no evidence that human superstition regarding bad luck Fridays affects precious metals markets in a negative way, i.e. returns on Fridays the 13th are not significantly lower than on regular Fridays. Second, besides showing robustness in a variety of settings, we can confirm this main result in a sensitivity check, where we replace the dummy variables by a new measure of investor attention, recently promoted by Da et al. (2011), that is based on Google search volumes. Third, as an important by-product of our study, we can show that there is significant evidence of time-varying skewness and kurtosis in precious metals returns.

Keywords:

• Friday the 13th
• GARCHSK
• Google search volumes
• precious metals

JEL Classification:

• G10
• Q30

Acknowledgement

The author thanks an anonymous reviewer for valuable comments that helped to significantly improve the article. Special gratitude also goes to Doaa Akl Ahmed for giving helpful insights into the implementation of the GARCHSK model.

Notes

¹ Recent studies also examine the relationship between gold and oil but do not find undisputable evidence (see Plourde and Watkins, 1998; Baffes, 2007; Sari et al., 2007; Zhang and Wei, 2010; Le and Chang, 2012).

² In contrast, contributions on seasonality in other commodities, equities, fixed income securities, real estate investment trusts and futures are rather numerous (see literature reviews in Lucey, 2004; Lucey and Tully, 2006).

³ Herbst and Maberly (1988) questioned the validity of these results. However, in a reply, Ma et al. (1989) refute this criticism and confirm the findings of Ma (1986).

⁴ See Brauer and Ravichandran (1986), Chang et al. (1990), Adrangi and Chatrath (2002), Lucey and Tully (2006), Chng (2009), Sari et al. (2010), Szakmary et al. (2010), Morales and Andreosso-O’Callaghan (2011), Arouri et al. (2012), Vivian and Wohar (2012), Creti et al. (2013) and Hammoudeh et al. (2010, 2011, 2013).

⁵ Anatolyev and Kryzhanovskaya (2009) provide an interesting application of the GARCHSK model. They use it for the directional prediction of returns under asymmetric loss.

⁶ An alternative to account for time-varying skewness and kurtosis would be the approach proposed by Jondeau and Rockinger (2003) and recently applied by Bali et al. (2008). It employs a conditional generalized Student-t distribution (based on the work of Hansen, 1994) to capture conditional skewness and kurtosis by imposing a time-varying structure for the two parameters that control its probability mass. However, these parameters do not follow a GARCH structure for either skewness or kurtosis.

⁷ Ahmed (2011) shows that more complex GARCH specifications for skewness and kurtosis (e.g. T-GARCH models) are inferior to the standard one.

⁸ This Gram–Charlier series expansion, where skewness and kurtosis directly appear as parameters, has become popular in finance as a generalization of the normal density (see Jondeau and Rockinger, 2001; León et al., 2009).

⁹ Note that, in the estimation process, the parameters of the variance and kurtosis equations are restricted to be nonnegative because variance and kurtosis have to take nonnegative values by definition.

¹⁰ An alternative approach for modelling time-varying mean and variance, but constant skewness and kurtosis, has been proposed by Premaratne and Bera (2000). They suggest capturing asymmetry and excess kurtosis with the Pearson type IV distribution (an approximation of the noncentral t-distribution proposed by Pearson and Merrington, 1958), which has three parameters that can be interpreted as volatility, skewness and kurtosis.

¹¹ In our application, an increase of the AR or GARCHSK order beyond the order of these final specifications does not significantly increase model fit (as measured by the Akaike information criterion).

¹² The time frame is determined by data availability and the fact that, for result comparability, the same period is used for all precious metals.

¹³ Unlike most of the previous studies, we do not exclude non-Friday returns because that would not allow full information GARCH modelling and thus deliver no adequate description of the return generating processes.

¹⁴ Extensive documentations on historic developments in precious metals markets are offered by the World Gold Council (www.gold.org), the Silver Institute (www.silverinstitute.org) and the International Precious Metal Institute (www.ipmi.org).

¹⁵ Higher-order models are often useful when a long span of data is used, like several decades of daily data (see Engle, 2001). With additional lags the models allow both fast and slow decay of information.

¹⁶ For gold, we encounter the problem that only after the inclusion of the insignificant variable lagged skewness (kurtosis), we are able to come up with nonautocorrelated cubed (fourth order of) standardized residuals. Also, note that, for other gold series available in Thomson Reuters Datastream (GOLDUSD and GOLDHAR), lagged skewness and kurtosis turn out to be significant.

¹⁷ Due to space considerations we concentrate on verbally summarizing their basic design and main implications. Detailed results can be made available upon request.

¹⁸ This is of interest because empirical results for broad equity and bond indices show that market declines forecast higher volatility than comparable market increases do (see Engle, 2001), while results for precious metals markets partially imply the opposite (see Bowden and Payne, 2008).

¹⁹ This approach is similar to Auer (2014b) who performs a sub-period seasonality analysis for the oil market using bull and bear periods defined by the Bespoke Investment Group.

²⁰ When fitting the models to weekly data, we find similar orders w, p, q, r, s, u and v as in the daily case.