Forecasting Oil Price by Hierarchical Shrinkage in Dynamic Parameter Models

Table 2

Descriptive statistics.

	WTI	BRENT	OD_CONS	OD_STOCKS	OS_WORLD	P_GOLD	US_EX
Mean	0.0009	0.0015	−0.0001	0.0003	0.0004	0.0028	0.0003
Median	0.0058	0.0069	−−0.0008	0.0005	0.0005	0.0027	0.0002
Maximum	0.0929	0.0851	0.0242	0.0090	0.0094	0.0537	0.0440
Minimum	−0.1442	−0.1351	−0.0264	−0.0086	−0.0064	−0.0904	−0.0178
Std. dev.	0.0389	0.0395	0.0107	0.0033	0.0029	0.0222	0.0070
Skewness	−0.8849	−0.9662	−0.0293	−2.2210	−0.0453	−0.4846	1.4488
Kurtosis (excess)	1.7698	1.5476	−0.5727	−0.0127	−0.1753	1.4502	8.2127
Jarque–Bera	46.7237	45.7129	2.4715	1.4584	0.2903	22.6911	565.6776
Q(20)	45.1300	40.8931	282.3031	108.7411	43.0371	27.1741	26.0612
PP test	−9.4826	−9.7966	−20.9879	−14.3289	−13.5263	−15.2111	12.0550
ADF	−6.6839	−9.7414	−3.2129	−3.7359	−7.0902	−15.1254	−11.9771
	SP500	P_GAS	VIX	IP_TOTAL	EPU	KILIAN	Google
Mean	0.0019	−0.0010	0.0010	0.0004	0.0035	13.7941	0.0046
Median	0.0045	−0.0034	−0.0072	−0.0005	0.0041	2.1302	0.0000
Maximum	0.0444	0.1649	0.3703	0.0162	0.2831	187.8978	0.3358
Minimum	−0.0806	−0.1766	−0.2111	−0.0222	−0.2448	−163.4310	−0.2320
Std. dev.	0.0172	0.0549	0.0887	0.0072	0.0835	79.2186	0.1000
Skewness	−1.0534	0.1095	0.6745	0.1728	0.3511	0.3115	0.8297
Kurtosis (excess)	3.1059	1.1509	1.5779	0.0032	1.2777	−0.7538	1.0399
Jarque–Bera	105.0568	10.2378	32.1443	0.8914	15.8510	7.1318	28.6037
Q(20)	40.0941	24.4420	33.8112	219.2882	33.3670	1659.5120	18.3661
PP test	−11.2842	−13.9759	−16.6098	−20.3007	−15.4433	−2.1650	−14.1582
ADF	−5.3398	−13.8972	−7.2381	−3.9125	−10.8053	−2.6820	−14.0785

Symbols , , and denote rejections of the null hypothesis at the 10%, 5%, and 1% significance levels, respectively. The Jarque–Bera statistic is used to test the null hypothesis of the normal distribution. Q(20) is the Ljung-Box Q statistics with lag order of 20. ADF refers to the statistics from the augmented Dickey–Fuller unit root tests. The entire sample period is from January 2004 to December 2018.