Modelling the oil price volatility and macroeconomic variables in South Africa using the symmetric and asymmetric GARCH models

Figures & data

Table 1. Descriptive statistics results

	Oil	Interest rate	Inflation	GDP	Exchange rate
Mean	73.453	10.715	7.219	0.578	7.240
Median	34.547	10.833	6.367	0.621	6.999
Maximum	1,213.483	21.687	16.167	1.837	15.857
Minimum	11.487	5.000	0.433	−1.530	2.534
Std. Dev.	148.070	4.382	3.551	0.681	3.272
Skewness	5.793	0.373	0.774	−0.529	0.543
Kurtosis	39.609	1.928	3.187	3.040	2.658
Jarque–Bera test	7,003.771	8.097	11.539	5.330	6.156
Probability	0.000	0.018	0.003	0.070	0.046
Sum	8,373.661	1,221.474	822.933	65.890	825.331
Sum Sq. Dev.	2,477.493	2,170.131	1,425.149	52.472	1,209.850
Observations	114	114	114	114	114

Figure 1. Time series plots at level.

Table 2. Stationarity test results

Variables	Level of test	ADF test statistic	p-value	PP test statistic	p-value	Conclusion
Oil	Level	−7.707	0.000	−7.821	0.000	Stationary
	1st Difference	−8.930	0.000	−52.828	0.000	Stationary
Interest rate	Level	−2.019	0.279	−1.702	0.428	Nonstationary
	1st Difference	−6.416	0.000	−5.873	0.000	Stationary
Inflation	Level	−2.929	0.045	−2.248	0.191	Nonstationary
	1st Difference	−5.085	0.000	−7.082	0.000	Stationary
GDP	Level	−5.327	0.000	−5.314	0.000	Stationary
	1st Difference	−8.901	0.000	−30.958	0.000	Stationary
Exchange rate	Level	−0.721	0.836	−0.907	0.783	Nonstationary
	1st Difference	−8.528	0.000	−8.528	0.000	Stationary

Figure 2. Residual time series plots.

Table 3. Parameter estimation results of the ARCH model

Variables	Coefficient	Std. Error	z-Statistic	Prob.
GDP	61.401	2.408	25.504	0.000
Inflation	13.364	0.387	34.521	0.000
Interest rate	−16.253	0.342	−47.471	0.000
Exchange rate	−5.453	0.256	−21.296	0.000
C	148.302	4.787	30.983	0.000
Variance equation
C	82.995	91.566	0.906	0.365
	7.511	0.827	9.083	0.000

Table 4. Parameter estimation results of the GARCH and EGARCH model

Model	Variables	Coefficient	Std. Error	z-Statistic	Prob.
GARCH	GDP	28.577	1.197	23.869	0.000
	Inflation	5.721	0.330	17.343	0.000
	Interest rate	−16.127	0.258	−62.615	0.000
	Exchange rate	−7.584	0.037	−206.236	0.000
	C	229.311	1.943	118.019	0.000
	Variance equation
	C	4.550	28.399	0.160	0.873
		11.838	0.770	15.369	0.000
		−0.0004	0.000	−0.818	0.413
EGARCH	GDP	−0.734	1.045	−0.703	0.482
	Inflation	−0.386	0.380	−1.014	0.311
	Interest rate	−7.228	0.414	−17.470	0.000
	Exchange rate	−2.029	0.259	−7.820	0.000
	C	125.816	3.318	37.921	0.000
	Variance equation
	Ω	−0.540	0.035	−15.386	0.000
		0.744	0.106	7.034	0.000
		−0.948	0.089	−10.678	0.000
		1.068	2.2E-104	4.8E+103	0.000

Table 5. Diagnostic test results

Oil Price		GARCH		EGARCH
Variable	Diagnostic tests	Statistics	p-value	Statistics	p-value
GDP	ARCH-LM	0.056	0.814	0.0003	0.987
	JB	3,508.024	0.000	2,940.838	0.000
	Box–Pierce test (R)	1.965	0.161	5.296	0.258
	Box–Ljung test (R^2)	2.178	0.156	5.540	0.236
Inflation	ARCH-LM	6.20e-05	0.099	4.81e-08	0.9998
	JB	15,692.89	0.000	6,255.761	0.000
	Box–Pierce test (R)	2.345	0.126	0.546	0.969
	Box–Ljung test (R^2)	2.407	0.120	0.569	0.966
Interest rate	ARCH-LM	0.009	0.926	0.003	0.956
	JB	25,507.08	0.000	12,060.64	0.000
	Box–Pierce test (R)	0.398	0.528	10.216	0.369
	Box–Ljung test (R^2)	0.408	0.523	10.501	0.033
Exchange rate	ARCH-LM	0.004	0.953	0.001	0.978
	JB	15,911.76	0.000	6,943.282	0.000
	Box–Pierce test (R)	0.090	0.764	1.538	0.820
	Box–Ljung test (R^2)	0.092	0.761	1.597	0.809