Return and volatility spillovers in equity markets: An investigation using various GARCH methodologies

Figures & data

Table 1. Descriptive statistics

	UK	Germany	Turkey	Russia	China
Mean	−0.009964	−0.000775	−0.033522	−0.070915	−0.016840
Median	0.044962	0.027719	0.079773	−0.069971	−0.014589
Maximum	4.872358	7.377567	8.240466	8.716479	6.460042
Minimum	−6.421240	−7.571491	−11.46181	−13.02545	−6.660969
Std. dev.	1.196827	1.556985	1.892570	1.993688	1.429756
Skewness	−0.405398	−0.230017	−0.440132	−0.434399	−0.126147
Kurtosis	5.327631	5.908301	6.206646	7.311265	5.969461
Jarque–Bera	315.4071	450.1094	574.0656	1004.162	461.0900
Probability	0.000000	0.000000	0.000000	0.000000	0.000000
Sum	−12.41532	−0.965906	−41.76804	−88.36059	−20.98228
Sum Sq. dev.	1,783.332	3,018.132	4,459.365	4,948.618	2,545.030
Observations	1,246	1,246	1,246	1,246	1,246

Figure 1. Graphs of daily returns of selected ETFs.

Table 2. Co-movements* of daily ETF returns (UK, Germany, Turkey, Russia and China)

$r_{t\left(UK\right)}=0.555r_{t\left(Germany\right)}+0.081r_{t\left(Russia\right)}+0.088r_{t\left(China\right)}-0.039r_{t-1\left(UK\right)}+0.023r_{t(Turkey)}+e_t$

$r_{t\left(Germany\right)}=1.000r_{t\left(UK\right)}+0.077r_{t\left(Turkey\right)}+0.053r_{t\left(Russia\right)}+e_t$

$r_{t\left(Turkey\right)}=0.310r_{t\left(Germany\right)}+0.241r_{t\left(Russia\right)}+0.179r_{t\left(UK\right)}+e_t$

$r_{t\left(Russia\right)}=0.517r_{t\left(UK\right)}+0.209r_{t\left(Turkey\right)}+0.229r_{t\left(China\right)}+0.202r_{t\left(Germany\right)}+e_t$

$r_{t\left(China\right)}=0.342r_{t\left(UK\right)}+0.164r_{t-1\left(Germany\right)}+0.143r_{t\left(Russia\right)}-0.135r_{t-1\left(China\right)}+0.172r_{t-1\left(UK\right)}+0.079r_{t-1(Russia)}+e_t$

* All coefficients are significant at the five percent level (p < 0.05); r and e denote returns and error terms, respectively.

Table 3. Volatility persistence

Coefficient	UK	Germany	Turkey	Russia	China
AR(1)				0.0548 (0.049)
Constant (ω)	0.0349 (0.004)	0.0167 (0.095)	0.1454 (0.017)	0.0504 (0.027)	0.0373 (0.004)
ARCH(−1) (α)	0.0935 (0.000)	0.0504 (0.000)	0.0770 (0.000)	0.0662 (0.000)	0.0605 (0.000)
GARCH(−1) (β)	0.8842 (0.000)	0.9426 (0.000)	0.8830 (0.000)	0.9231 (0.000)	0.9221 (0.000)
α + β < 1	0.9777	0.9930	0.9600	0.9893	0.9826
AIC	2.973977	3.457890	3.990026	3.993665	3.326480
SIC	2.994553	3.478466	4.010602	4.018357	3.347057
ARCH-LM test statistic (Obs*R^2)	0.404462	1.255601	0.140018	0.409781	2.611150
Prob. χ^2(1)	0.5248	0.2625	0.7083	0.5221	0.1061

Figure 2. GARCH graph of ETF returns for UK

Figure 3. Variances of ETF returns: All.

Figure 4. Variances of ETF returns: China, Germany and UK.

Figure 5. Variances of ETF returns: China, Russia and Turkey.

Table 4. Estimation results of GARCH-M (1, 1)

	UK	Germany	Turkey	Russia	China
@SQRT(GARCH) (δ)	0.3047 (0.0009)	0.0737 (0.4430)	−0.1186 (0.3906)	0.1545 (0.1062)	−0.0124 (0.9068)
Constant (ω)	0.0381 (0.0046)	0.0169 (0.0961)	0.1472 (0.0162)	0.0494 (0.0258)	0.0371 (0.0378)
ARCH(−1) (α)	0.0977 (0.0000)	0.0509 (0.0001)	0.0795 (0.0001)	0.0655 (0.0000)	0.0604 (0.0002)
GARCH(−1) (β)	0.8778 (0.0000)	0.9420 (0.0000)	0.8803 (0.0000)	0.9241 (0.0000)	0.9225 (0.0000)
α + β < 1	0.9755	0.9930	0.9598	0.9896	0.9829
AIC	2.968004	3.459033	3.990958	3.994712	3.328071
SIC	2.992696	3.483725	4.015650	4.019404	3.352763

Table 5. Estimation results of EGARCH

	UK	Germany	Turkey	Russia	China
AR(1)				0.0563 (0.0348)
Constant (ω)	−0.0418 (0.0030)	−0.0527 (0.0012)	−0.0436 (0.0354)	0.0009 (0.9286)	−0.0669 (0.0002)
|(RES(−1)|/@SQRT (GARCH(−1)) (α)	0.0627 (0.0010)	0.0761 (0.0006)	0.1485 (0.0000)	0.0094 (0.4806)	0.1096 (0.0000)
RES(−1)/@SQRT (GARCH(−1)) (γ)	−0.1379 (0.0000)	−0.0745 (0.0000)	−0.0994 (0.0000)	−0.1098 (0.0000)	−0.0715 (0.0000)
LOG(GARCH(−1)) (β)	0.9672 (0.0000)	0.9896 (0.0000)	0.9395 (0.0000)	0.9940 (0.0000)	0.9766 (0.0000)
AIC	2.987166	3.437808	4.020180	3.949949	3.316318
SIC	3.007742	3.462500	4.040757	3.978756	3.341010
ARCH-LM test statistic (Obs*R^2)	0.869965	0.446397	0.861121	1.414937	0.391164
Prob. Chi-Square(1)	0.3510	0.5041	0.3534	0.2342	0.5317

Table 6. Volatility transmission

Coefficient	UK	Germany	Turkey	Russia	China
Variance equation
Constant (ω)	0.0265 (0.034)	0.0124 (0.109)	0.1328 (0.023)	0.4088 (0.000)	0.7437 (0.000)
ARCH(−1) (α)	0.0842 (0.000)	0.0353 (0.000)	0.0727 (0.000)	0.1187 (0.000)	0.0821 (0.000)
GARCH(−1) (β)	0.8819 (0.000)	0.9414 (0.000)	0.8859 (0.000)	0.7464 (0.000)	0.5661 (0.000)
$r_{t-1(UK)}^2$		0.0338 (0.004)	−0.0297 (0.461)	0.0544 (0.211)	0.0154 (0.455)
$r_{t-1(Germany)}^2$	0.0017 (0.876)		2.67E-05 (0.998)	0.0082 (0.716)	0.0122 (0.247)
$r_{t-1(Turkey)}^2$	0.0012 (0.486)	0.0019 (0.054)		−0.0179 (0.000)	−0.0138 (0.000)
$e_{t-1(Russia)}^2$	7.12E-05 (0.9781)	−0.0018 (0.089)	0.0036 (0.6225)		−0.0073 (0.000)
$r_{t-1(China)}^2$	0.0083 (0.346)	−0.0026 (0.6181)	0.0223 (0.318)	0.0525 (0.000)
AIC	2.979171	3.493761	3.994777	4.084182	3.464633
SIC	3.016233	3.526705	4.031839	4.117126	3.497577

Note: r and e denote returns and error terms, respectively.