On the role of structural breaks in identifying the dynamic conditional linkages between stock and commodity markets

Tarek Chebbi; Abdelkader Derbali

The relationship between commodity and stock markets has been extensively scrutinized and documented in the literature. In particular, some papers have used the dynamic conditional correlation–generalized autoregressive conditional heteroscedasticity (DCC–GARCH) methodology to estimate the links between both markets (Creti et al 2013; Sadorsky 2014; Chebbi and Derbali 2016). However, most studies focused on a general assumption that the unconditional variance of the underlying series is constant, implying that volatility is generated by a stable GARCH process. We all know that markets often experience structural breaks in the unconditional variance that causes breaks in the GARCH parameters. These structural breaks in volatility may be caused by political events, social events, country-specific economic events or regional and global events (eg, the 2007–8 financial crisis, the European sovereign debt crisis, the 2011 Arab Spring, etc). These findings are consistent with the work of Ewing and Malik (2010), who find supportive evidence that there are structural breaks in variance in oil prices. On a related note, Perron and Qu (2010) confirm the presence of structural breaks on stock returns. In a recent paper, Ewing and Malik (2016) have introduced structural breaks into univariate and bivariate GARCH models and have found strong evidence of significant spillovers of volatility between oil prices and the US stock market.

It is particularly important to recognize that none of the recent studies has focused on estimating dynamic conditional correlations using a DCC–GARCH specification with structural breaks. All this recent research focuses on examining the impact of structural breaks on a univariate GARCH model (ie, accurately capturing the impact of news on volatility in each individual market) or on bivariate GARCH models, in order to accurately estimate the volatility spillovers across markets.

In this paper, we fill this gap in the research and extend the small amount of literature to date by making several contributions. First, a novel aspect of our paper is that it studies the time-varying correlations between commodity and Islamic stock markets. We do this by introducing the detected structural breaks into our DCC–GARCH model in order to accurately capture the impact of shocks on such correlations. An interesting paper that is closely related to ours is that by Mensi et al (2015). This study examines DCC–fractionally integrated asymmetric power autoregressive conditional heteroscedasticity (FIAPARCH) under structural breaks to estimate the correlation between commodity futures and Saudi markets. While our paper employs the same approach, we complement the findings of this paper by showing strong evidence of significant links between oil and gas prices and the Qatar Exchange (QE) Al Rayan Islamic Index. Second, in discussing the links between commodity and stock markets, it is useful to differentiate between exporting and importing countries. None of the above-mentioned literature has studied the link between commodities and the Islamic stock index, for example, for exporting countries that depend mostly on their energy sector. In particular, our paper analyzes a large sample, composed of two strategic commodities covering energy sectors (crude oil and natural gas) and an Islamic index launched by the QE and Al Rayan Investment: the QE Al Rayan Islamic Index, over the period March 15, 2011–December 25, 2014. Based on this large data set, we also try to examine how the two strategic commodities constitute a homogeneous asset class.

The contributions of our paper are summarized as follows. Our most important finding is that both markets are time varying and highly volatile when we take the structural breaks in the DCC approach into account. Interestingly, we detect two structural breaks for the DCC between the Al Rayan Islamic Index and crude oil, on November 2, 2011 and December 5, 2012; and three structural breaks for the DCC between the Al Rayan Islamic Index and natural gas, on October 30, 2011, October 9, 2012 and January 30, 2014. From our empirical results, the strong links between both markets are suggestive of the importance of the financialization of commodities. This may be behind the increased interest in commodities from investors. Finally, the analysis of the behavior of each commodity with regard to the Islamic stock index supports the idea that commodities cannot be viewed as a homogeneous asset class.

The rest of our paper is organized as follows. Section 2 describes the econometric methodology. Section 3 defines the data used in this study. Section 4 discusses the results. Section 5 offers some concluding remarks.

2 Econometric methodology

In this section, we present methodologically how we can identify structural breaks in DCC.

The DCC–GARCH(1,1) is given by the following:

Q_{t}=\omega+\alpha{\varepsilon_{t-1}}\varepsilon_{t-1}^{\prime}+\beta Q_{t-1},

(2.1)

where $\omega=(1-\alpha-\beta)\bar{Q}$ , with $\bar{Q}$ being the unconditional covariance of the standardized disturbances ${\varepsilon_{t}}$ ; $\omega$ , $\alpha$ and $\beta$ are the estimated parameters.

Lamoureux and Lastrapes (1990) found that the standard GARCH models overestimate the volatility persistence, as they ignore structural breaks; these breaks should be incorporated into GARCH models to obtain accurate parameter estimates. Consequently, we extend our bivariate GARCH(1,1) model with structural breaks, and this is expressed as follows:

h_{t}=\omega+{d_{1}}{D_{1}}+\cdots+{d_{n}}{D_{n}}+\alpha\varepsilon_{t-1}^{2}+% \beta{h_{t-1}},

(2.2)

where $D_{1}$ , $D_{n}$ , are a set of dummy variables that take a value of $1$ from each structural breakpoint onwards, and $0$ elsewhere.

In this paper, we contribute to the literature by including structural breaks in our DCC–GARCH(1,1) models. The DCC–GARCH(1,1) with structural breaks is given as follows:

Q_{t}=\omega+{d_{1}}{D_{1}}+\cdots+{d_{n}}{D_{n}}+\alpha{\varepsilon_{t-1}}% \varepsilon_{t-1}^{\prime}+\beta{Q_{t-1}},

(2.3)

where $D_{1}$ , $D_{n}$ , are a set of dummy variables that take a value of $1$ from each structural breakpoint onwards, and $0$ elsewhere.

3 Data

The data employed in this paper is made up of daily spot price series associated with the Al Rayan Islamic Index and two energy commodities: crude oil and natural gas. Our daily data runs from March 15, 2011 to December 25, 2014.

Table 1 shows the main statistical features for the daily returns series. We observe that the lowest average of return is for crude oil, while the highest average is for the Al Rayan Islamic Index; this is followed by natural gas with a value of 0.000177. Looking at the volatility of the daily return series, as measured by the standard deviation, natural gas exhibits a daily volatility of 0.026172; this is compared with crude oil, which has a value of 0.015674. The lowest volatility is for the Al Rayan Islamic Index, which has a value of 0.009524. The values of skewness (asymmetry) and kurtosis (flatness) for the various variables suggest that the distributions of output are not normally distributed. This is indicated by the Jarque–Bera test, which rejects the null assumption of the normality of the series of the outputs to a threshold of 1%. These values give good reason for working with the GARCH approach.

Table 1: Descriptive statistics for daily returns. [The main statistical features of the daily price returns for the Al Rayan Islamic Index, crude oil and natural gas series over the period from March 15, 2011 to December 25, 2014. Significant at a threshold value of (*) 1%. SD denotes standard deviation; JB denotes Jarque–Bera.]

	Mean	Median	Max	Min	SD	Skewness	Kurtosis	JB	Prob	Obs.
Al Rayan	0.000973	0.001095	0.089378	$-$ 0.081982	0.009524	$-$ 0.020125	21.62040	13579.90*	0	940
Islamic Index
Crude oil	$-$ 0.000299	0.000496	0.089454	$-$ 0.090379	0.015674	$-$ 0.312934	06.611637	00526.2289*	0	940
Natural gas	0.000177	$-$ 0.000274	0.132673	$-$ 0.119312	0.026172	0.261034	05.249737	00208.9099*	0	940

We present in Table 2 the main statistical features for the conditional correlation between the Islamic index and energy commodities. We can show that, on average, the correlation between the Al Rayan Islamic Index and natural gas (0.314437) is greater than the correlation between the Al Rayan Islamic Index and crude oil (0.294889). A possible explanation for this is associated with the importance of the energy sector to the story of Qatari growth. More specifically, it should be noted that Qatar is a member of the Organization of the Petroleum Exporting Countries (OPEC), and it is among the largest natural gas exporters, and possesses the largest reserves, in the world. It is well recognized that stock markets are dependent on the economy; therefore, oil price changes appear to have a significant effect on stock prices (see Jones and Kaul 1996).

Table 2: Descriptive statistics for DCC–GARCH(1,1). [The main statistical features of the DCC between the Al Rayan Islamic Index and energy commodities (crude oil and natural gas) during the period from March 15, 2011 to December 25, 2014. Significant at a threshold value of (*) 1%. SD denotes standard deviation; JB denotes Jarque–Bera.]

	Mean	Median	Max	Min	SD	Skewness	Kurtosis	JB	Prob	Obs.
DCC: Al Rayan	0.294889	0.271236	0.788058	0.174101	0.096090	1.948357	07.768236	1485.218*	0	940
Islamic Index/
crude oil
DCC: Al Rayan	0.314437	0.294544	0.693362	0.243967	0.063822	2.446774	10.35900	3058.984*	0	940
Islamic Index/
natural gas

In Figures 1, 2 and 3, we present the evolution of the Islamic index and energy commodity return series. It can be seen that the Al Rayan Islamic Index and natural gas present three observed breaks, while crude oil displays two observed breaks.

Figure 1: Volatility of Al Rayan Islamic index returns with breaks over the period March 15, 2011–December 25, 2014.

Figure 2: Volatility of crude oil returns with breaks over the period March 15, 2011–December 25, 2014.

Figure 3: Volatility of natural gas returns with breaks over the period March 15, 2011–December 25, 2014.

4 Empirical findings

In order to investigate the structure of conditional correlations between two energy commodity markets and the Al Rayan Islamic Index by allowing for structural breaks, the DCC approach of Engle (2002) is employed over the period March 15, 2011–December 25, 2014.

An important issue for any paper studying the implications of structural breaks in the volatility models – and, thus, for the improvement of the estimation results – is the identification of the structural breakpoints in the unconditional variance. Table 3 reports the structural breaks estimated in conditional correlation between the Islamic index and energy commodities. From this table, we can see that the conditional correlation between the Al Rayan Islamic Index and crude oil presents two breakpoints on two different dates: November 2, 2011 and December 5, 2012. The conditional correlation between the Al Rayan Islamic Index and natural gas presents three breakpoints on three different dates: October 30, 2011, October 9, 2012 and January 30, 2014. These dates are obtained using DCC–GARCH(1,1) models with breaks.

Table 3: Structural breaks in DCC. [Time periods detected during a sample period from March 15, 2011 to December 25, 2014. Significant at a threshold value of (*) 1%.]

Series	points	Time period	SD	Prob
	Break-
DCC: Al Rayan	2	Mar 15, 2011–Nov 2, 2011	0.021213	0.0000*
Islamic Index/		Nov 3, 2011–Dec 5, 2012	0.009932	0.0000*
crude oil		Dec 5, 2012–Dec 25, 2014	0.017293	0.0000*
DCC: Al Rayan	3	Mar 15, 2011–Oct 30, 2011	0.005483	0.0000*
Islamic Index/		Oct 31, 2011–Oct 9, 2012	0.011864	0.0000*
natural gas		Oct 10, 2012–Jan 30, 2014	0.013801	0.0000*
		Feb 2, 2014–Dec 25, 2014	0.002561	0.0000*

In Table 4, we present the empirical results from the DCC–GARCH(1,1) model without and with structural breaks. From this table, we can see that all parameters are highly significant, with a volatility persistence of 0.924429 for the conditional correlation between the Al Rayan Islamic Index and the crude oil series, and a volatility persistence of 0.993809 for that between the Al Rayan Islamic Index and the natural gas correlation series, if structural breaks are ignored. Moreover, the small difference between the two levels of volatility persistence can be simply explained by the fact that commodities cannot be viewed as a homogeneous asset class (Creti et al 2013).

Table 4: Estimation results for DCC–GARCH models without and with structural breaks. [The

p

-values in parenthesis are based on robust standard errors calculated from the method given by Bollerslev and Wooldridge (1992).

\alpha+\beta

measures the volatility persistence. Half-life gives the point estimate of half-life (

j

) in days given as

\smash{(\alpha+\beta)j=\tfrac{\text{1}}{\text{2}}}

. The estimated variance equation without structural breaks for the GARCH model is

\smash{h_{t}=\alpha_{\text{0}}+\alpha_{\text{1}}\varepsilon_{t-\text{1}}^{% \text{2}}+{\beta}_{\text{1}}h_{t-\text{1}}}

. The estimated DCC equation without structural breaks for the GARCH model is

\smash{Q_{t}=\omega+\alpha\varepsilon_{t-\text{1}}\varepsilon_{t-1}^{{}^{% \prime}}+\beta{Q}_{t-\text{1}}}

. Two dummy variables were used for the DCC–GARCH(1,1) model between the Al Rayan Islamic Index and crude oil with structural breaks; the coefficients (

p

-values) were

-

0.0062561 (0.0000) and

-

0.0043449 (0.0000). Three dummy variables were used for the DCC–GARCH (1,1) model between the Al Rayan Islamic Index and natural gas with structural breaks; the coefficients (

p

-values) were 0.017006 (0.0000), 0.018515 (0.0000) and

-

0.007717 (0.0000). Significant at threshold values of (*) 1% and of (**) 5%.]

(a) DCC: Al Rayan Islamic Index/crude oil

	Parameters

					Half-life	Log-
	$\omega$	$\alpha$	$\beta$	$\alpha+\beta$	(days)	likelihood
Breaks	0.000090	0.025417	0.899012	0.924429	8.82	5614.737
ignored	(0.0000)*	(0.0000)*	(0.0000)*
Breaks	0.000090	0.004361	0.897741	0.902102	6.73	5615.642
accounted	(0.0000)*	(0.0000)*	(0.0000)*
for

(b) DCC: Al Rayan Islamic Index/natural gas
	Parameters

					Half-life	Log-
	$\omega$	$\alpha$	$\beta$	$\alpha+\beta$	(days)	likelihood
Breaks	0.000683	0.040499	0.953310	0.993809	111.61	5133.801
ignored	(0.0159)**	(0.0000)*	(0.0000)*
Breaks	0.000683	0.040441	0.953161	0.993602	107.99	5134.352
accounted	(0.0000)*	(0.0000)*	(0.0000)*
for

The results reported in Table 4 complement the existing literature by assessing the response of the links between commodity and stock markets to the inclusion of structural breaks. As can be seen, we find evidence that all parameters are statistically significant, confirming that the links between both markets are time varying and highly volatile. In addition, there is evidence that the sum of the volatility coefficients ( $\alpha+\beta$ ) is very close to unity, namely for the Al Rayan Islamic Index/natural gas case, as shown; this proves the higher persistence of volatility between the Islamic stock market and commodity markets. One possible explanation is that such persistence goes along with the financialization of commodities (Creti et al 2013).

One might argue that our results highlight the importance of including structural breaks in modeling the time-varying conditional correlations. However, the results from estimating the DCC–GARCH(1,1) model are sensitive to the inclusion of structural breaks. The volatility persistence decreases by its lowest amount for the correlation between the Islamic stock market index and energy commodities following the incorporation of structural breaks, a result which is consistent with earlier studies. More specifically, when we consider the effect of structural breaks on correlation series, we can show that conditional correlations between the Al Rayan Islamic Index and crude oil appear to respond much more than the other series.

Finally, our results also show that the estimated half-life of shocks changes, decreasing from about eight days to about six days for the dynamic correlation between the Al Rayan Islamic Index series and the crude oil series, and from about 111 days to about 107 days for the other correlation series.

5 Conclusion

In this paper, we explore the time-varying linkages between two strategic commodities covering the energy sector (crude oil and natural gas) and the QE Al Rayan Islamic Index over the period March 15, 2011–December 25, 2014. For this purpose, we consider the DCC–GARCH approach with structural breaks. The results in this paper indicate strong, significant DCCs between both markets if structural breaks are incorporated into the variance. These findings have confirmed the importance of the financialization of commodity markets. However, the estimated results highlight that the persistence of volatility is sensitive to the inclusion of structural breaks in the DCC–GARCH(1,1) model. The conditional correlations between the Al Rayan Islamic Index and natural gas appear to respond much more than the other series. We conclude that the behavior of each commodity with regard to stock market fluctuations reflects the idea that commodities cannot be viewed as a homogeneous asset class. Finally, our study covers an important topic for policy makers and portfolio risk managers. From a policy-making point of view, having accurate estimates of the volatility spillovers across markets is a critical step in making effective policy decisions. From the perspective of portfolio risk managers, our results are consistent with the notion of cross-market hedging.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

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