Table 9 Panel cointegration and VECM...

Table 9

Panel cointegration and VECM results

(a) Johansen Fisher panel cointegration test
# Of cointegtation	Fisher stat (trace)	Prob	Significance	Fisher stat (max-eigen)	Prob	Significance
None	472.5	0.0000	***	176.4	0.0000	***
At most 1	209.1	0.0000	***	153.3	0.0000	***
At most 2	80.9	0.0000	***	57.6	0.0000	***
At most 3	34.5	0.0006	***	21.6	0.0420	**
At most 4	16.7	0.1617		10.1	0.6040
At most 5	9.4	0.6725		5.2	0.9503
At most 6	6.5	0.8881		3.2	0.9940
At most 7	5.6	0.9330		4.2	0.9793
Lags: 1 to 7, N = 7,206, linear deterministic trend

(a) Johansen Fisher panel cointegration test
# Of cointegtation	Fisher stat (trace)	Prob	Significance	Fisher stat (max-eigen)	Prob	Significance
None	472.5	0.0000	***	176.4	0.0000	***
At most 1	209.1	0.0000	***	153.3	0.0000	***
At most 2	80.9	0.0000	***	57.6	0.0000	***
At most 3	34.5	0.0006	***	21.6	0.0420	**
At most 4	16.7	0.1617		10.1	0.6040
At most 5	9.4	0.6725		5.2	0.9503
At most 6	6.5	0.8881		3.2	0.9940
At most 7	5.6	0.9330		4.2	0.9793
Lags: 1 to 7, N = 7,206, linear deterministic trend

(b) VECM results for log(price), standard errors in ( ), t-statistics in [ ]
	Coefficient	Std. error	t-statistic	Prob	Significance
LPRICE (−1)	0.0002	0.0000	3.8650	0.0001	***
ΔYield_30Y (−1)	0.0045	0.0019	2.3803	0.0173	**
ΔYield_10Y (−1)	(0.0033)	0.0013	(2.5542)	0.0106	**
ΔLPRICE (−1)	0.0331	0.0122	2.7228	0.0065	***
ΔLPRICE (−2)	0.0307	0.0121	2.5320	0.0113	**
ΔLPRICE (−4)	0.0279	0.0121	2.3094	0.0209	**
ΔYield_30Y (−2)	(0.1579)	0.0615	(2.5685)	0.0102	**
ΔYield_30Y (−3)	(0.1351)	0.0616	(2.1938)	0.0283	**
ΔYield_10Y (−2)	0.1593	0.0638	2.4954	0.0126	**
ΔYield_10Y (−4)	(0.1088)	0.0638	(1.7054)	0.0881	*
ΔYield_3m (−3)	(0.0997)	0.0361	(2.7579)	0.0058	***
ΔYield_3m (−4)	0.0922	0.0363	2.5377	0.0112	**
R_Gold (−2)	0.5357	0.1109	4.8296	0.0000	***
R_Gold (−3)	(0.4137)	0.1118	(3.7001)	0.0002	***
R_Gold (−5)	(0.4196)	0.1092	(3.8445)	0.0001	***
ΔVIX (−2)	(0.0040)	0.0007	(5.3939)	0.0000	***
ΔVIX (−4)	(0.0013)	0.0008	(1.7031)	0.0885	*
ΔVIX (−5)	0.0013	0.0008	1.7151	0.0863	*
R_SP500 (−2)	(0.0003)	0.0001	(2.0064)	0.0448	**
R_SP500 (−3)	0.0004	0.0001	3.0052	0.0027	***
R_SP500 (−5)	(0.0004)	0.0001	(2.9706)	0.0030	***
R_World (−1)	0.0006	0.0002	2.6606	0.0078	***
R_World (−2)	(0.0004)	0.0002	(1.8938)	0.0583	*
R_World (−4)	0.0008	0.0002	3.5133	0.0004	***
R_World (−5)	(0.0002)	0.0001	(2.3825)	0.0172	**
R_EM (−1)	(0.0005)	0.0001	(3.5521)	0.0004	***
ΔVolatility_5d (−4)	(0.0881)	0.0180	(4.9056)	0.0000	***
ΔVolatility_5d (−5)	(0.0306)	0.0179	(1.7071)	0.0878	*
Constant	0.0018	0.0009	2.1340	0.0328	**

(b) VECM results for log(price), standard errors in ( ), t-statistics in [ ]
	Coefficient	Std. error	t-statistic	Prob	Significance
LPRICE (−1)	0.0002	0.0000	3.8650	0.0001	***
ΔYield_30Y (−1)	0.0045	0.0019	2.3803	0.0173	**
ΔYield_10Y (−1)	(0.0033)	0.0013	(2.5542)	0.0106	**
ΔLPRICE (−1)	0.0331	0.0122	2.7228	0.0065	***
ΔLPRICE (−2)	0.0307	0.0121	2.5320	0.0113	**
ΔLPRICE (−4)	0.0279	0.0121	2.3094	0.0209	**
ΔYield_30Y (−2)	(0.1579)	0.0615	(2.5685)	0.0102	**
ΔYield_30Y (−3)	(0.1351)	0.0616	(2.1938)	0.0283	**
ΔYield_10Y (−2)	0.1593	0.0638	2.4954	0.0126	**
ΔYield_10Y (−4)	(0.1088)	0.0638	(1.7054)	0.0881	*
ΔYield_3m (−3)	(0.0997)	0.0361	(2.7579)	0.0058	***
ΔYield_3m (−4)	0.0922	0.0363	2.5377	0.0112	**
R_Gold (−2)	0.5357	0.1109	4.8296	0.0000	***
R_Gold (−3)	(0.4137)	0.1118	(3.7001)	0.0002	***
R_Gold (−5)	(0.4196)	0.1092	(3.8445)	0.0001	***
ΔVIX (−2)	(0.0040)	0.0007	(5.3939)	0.0000	***
ΔVIX (−4)	(0.0013)	0.0008	(1.7031)	0.0885	*
ΔVIX (−5)	0.0013	0.0008	1.7151	0.0863	*
R_SP500 (−2)	(0.0003)	0.0001	(2.0064)	0.0448	**
R_SP500 (−3)	0.0004	0.0001	3.0052	0.0027	***
R_SP500 (−5)	(0.0004)	0.0001	(2.9706)	0.0030	***
R_World (−1)	0.0006	0.0002	2.6606	0.0078	***
R_World (−2)	(0.0004)	0.0002	(1.8938)	0.0583	*
R_World (−4)	0.0008	0.0002	3.5133	0.0004	***
R_World (−5)	(0.0002)	0.0001	(2.3825)	0.0172	**
R_EM (−1)	(0.0005)	0.0001	(3.5521)	0.0004	***
ΔVolatility_5d (−4)	(0.0881)	0.0180	(4.9056)	0.0000	***
ΔVolatility_5d (−5)	(0.0306)	0.0179	(1.7071)	0.0878	*
Constant	0.0018	0.0009	2.1340	0.0328	**

(c) VECM equation stats
	N	R²	Adjusted R²
LPRICE	7,146	0.0527	0.0450
ΔYield_30Y	7,142	0.1288	0.1216
ΔYield_10Y	7,142	0.1013	0.0939
ΔYield_3M	7,142	0.1951	0.1885
R_Gold	7,146	0.1650	0.1582
ΔVIX	7,146	0.1921	0.1855
R_SP500	7,146	0.2072	0.2007
R_World	7,146	0.9533	0.9529
R_EM	7,146	0.4843	0.4801
ΔVolatility_5d	7,146	0.2270	0.2207
ΔVolume	7,146	0.1724	0.1657

(c) VECM equation stats
	N	R²	Adjusted R²
LPRICE	7,146	0.0527	0.0450
ΔYield_30Y	7,142	0.1288	0.1216
ΔYield_10Y	7,142	0.1013	0.0939
ΔYield_3M	7,142	0.1951	0.1885
R_Gold	7,146	0.1650	0.1582
ΔVIX	7,146	0.1921	0.1855
R_SP500	7,146	0.2072	0.2007
R_World	7,146	0.9533	0.9529
R_EM	7,146	0.4843	0.4801
ΔVolatility_5d	7,146	0.2270	0.2207
ΔVolume	7,146	0.1724	0.1657

Note(s): Dependent variable: log(price). Cointegration results are in panel (a), VECM results are obtained using seven lags and three cointegrated terms in panel (b) and VECM R² in panel (c). Three cointegrated terms identified in panel (a) are expanded in panel (b). Panel (c) shows a much higher R² for the VECM than the OLS, FEM and REM. Significance at the 10, 5 and 1% levels are indicated by *, ** and ***, respectively. The date range is from 12/31/2013 to 08/01/2020

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