I have found Cointegration based on Engle/ Granger and Johansen. However, Granger-causality is rejected for both variables. How is that possible?
According to theory,
if x and y are I(1) and cointegrated, x is Granger causal to y and/or y is Granger causal to x.
However, Granger-causality has been rejected in my bivariate case, despite their cointegration relationship.
Did I understand it correctly that there has to be at least one granger causality flow in a bivariate cointegrated system?
Thank you for your answer!
Applying an VECM, I get the following results: with only the -0.022460 being significant…
Vector Error Correction Estimates
Date: 10/28/13 Time: 23:58
Included observations: 1113 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
CAD(-1) 1.000000
NATGAS(-1) 0.067366
(0.02646)
[ 2.54615]
C -0.077093
Error Correction: D(CAD) D(NATGAS)
CointEq1 -0.022460 -0.006601
(0.00514) (0.01384)
[-4.37213] [-0.47714]
D(CAD(-1)) -0.054710 0.029241
(0.02998) (0.08073)
[-1.82508] [ 0.36220]
D(CAD(-2)) 0.035656 0.101838
(0.02996) (0.08070)
[ 1.18998] [ 1.26200]
D(NATGAS(-1)) -0.004642 -0.077700
(0.01120) (0.03016)
[-0.41449] [-2.57591]
D(NATGAS(-2)) 0.004712 0.056858
(0.01120) (0.03016)
[ 0.42067] [ 1.88491]
C 0.000176 -0.000850
(0.00019) (0.00051)
[ 0.92332] [-1.65571]
R-squared 0.022437 0.011948
Best Answer
If there is cointegration, then there is (100% percent surely) G-causality, but not vice versa.
For stationarity check, one MUST use Narayan-Popp 2010 non-stationarity test that takes the possible existence of structural breaks in the data into account.
You have 1113 observations after adjustments. This implies about 3-year period. During that period, it is highly likely that crises/interventions occured. These are encoded as structural breaks.
For cointegration check, (in the case of possible structural breaks) one MUST use Johansen-Mosconi-Nielsen 2000 critical values rather than Osterwald-Lenum 1992 critical values.
So, I am of the opinion that if you employ true methods, you will most probably end up with either of the following cases:
1. Your variables are not all I(1); hence, cointegration is impossible.
2. Your variables are all I(1); but, they are not cointegrated.
If I had your data in my hand, I would be able to say which one of the cases is valid.
Note also that one-to-one applying of Joyeux 2007 method via R revealed that Eviews miscalculate cointegration check. Hence, use R no matter what...