johansen cointegration test
Posted: Mon Jul 26, 2010 3:10 pm
Hi!
I am currently conducting johansen tests for energy prices, energy consumption (total energy, electricy and oil) , gdp over 28 i determine the lag lenth trhough var lag order criteria (below eviexs output),
after that, I obtained the following johansen cointegration results. The Max-eigenvalue test indicates 4 cointegrating equation(s) at the 5% level and only 1 cointegrating equation(s) at the 1% level.
I am wondering if the high values for the trace and the max. eigenvalue are "normal" or if they are caused by some misspecification or wrong lag length. (below one eviews output)
why i obtained two differents results from the The Max-eigenvalue at 1% and 5%?
What results can i retain?
VAR Lag Order Selection Criteria
Endogenous variables: GDP TOTALENER ELEC PETROL ENERPRICE
Exogenous variables: C
Date: 07/20/10 Time: 03:38
Sample: 1980 2008
Included observations: 27
Lag LogL LR FPE AIC SC HQ
0 60.92141 NA 1.09E-08 -4.142327 -3.902357 -4.070971
1 189.2577 199.6342 5.38E-12 -11.79687 -10.35705* -11.36873
2 223.2814 40.32442* 3.41E-12* -12.46529* -9.825623 -11.68038*
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
Date: 07/20/10 Time: 04:22
Sample(adjusted): 1983 2008
Included observations: 26 after adjusting endpoints
Trend assumption: No deterministic trend (restricted constant)
Series: GDP TOTALENER ELEC PETROL ENERPRICE
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test
Hypothesized Trace 5 Percent 1 Percent
No. of CE(s) Eigenvalue Statistic Critical Value Critical Value
None ** 0.873969 133.8001 76.07 84.45
At most 1 ** 0.693950 79.94806 53.12 60.16
At most 2 ** 0.582673 49.16386 34.91 41.07
At most 3 ** 0.575145 26.44282 19.96 24.60
At most 4 0.148729 4.186644 9.24 12.97
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Trace test indicates 4 cointegrating equation(s) at both 5% and 1% levels
Hypothesized Max-Eigen 5 Percent 1 Percent
No. of CE(s) Eigenvalue Statistic Critical Value Critical Value
None ** 0.873969 53.85201 34.40 39.79
At most 1 * 0.693950 30.78420 28.14 33.24
At most 2 * 0.582673 22.72104 22.00 26.81
At most 3 ** 0.575145 22.25618 15.67 20.20
At most 4 0.148729 4.186644 9.24 12.97
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Max-eigenvalue test indicates 4 cointegrating equation(s) at the 5% level
Max-eigenvalue test indicates 1 cointegrating equation(s) at the 1% level
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
GDP TOTALENER ELEC PETROL ENERPRICE C
-31.74070 16.53381 7.421725 1.980752 -0.518644 378.9193
3.968486 3.876127 5.737066 2.301376 -22.42228 -137.7058
-18.48685 25.80403 -2.431289 -2.300829 11.71328 49.62418
77.08022 -23.82520 -25.18183 -8.709145 12.65383 -1092.401
18.11751 9.239821 -7.139590 3.571202 -22.04718 -425.2288
Unrestricted Adjustment Coefficients (alpha):
D(GDP) -0.013829 -0.001629 0.010892 -0.000251 -0.005922
D(TOTALENER) -0.010860 0.006783 -0.020469 -0.008886 -0.008570
D(ELEC) -0.060199 -0.034900 0.008717 -0.014779 0.013580
D(PETROL) -0.013942 -0.032427 -0.018786 0.028701 -0.032557
D(ENERPRICE) -0.015633 0.031859 0.003272 0.034608 -0.001624
1 Cointegrating Equation(s): Log likelihood 227.7175
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 -0.520903 -0.233824 -0.062404 0.016340 -11.93796
(0.08487) (0.03424) (0.02399) (0.11421) (0.96212)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.438927
(0.17784)
D(TOTALENER) 0.344706
(0.31029)
D(ELEC) 1.910771
(0.52012)
D(PETROL) 0.442528
(0.84806)
D(ENERPRICE) 0.496209
(0.49285)
2 Cointegrating Equation(s): Log likelihood 243.1096
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.350330 0.161005 -1.954544 -19.85496
(0.14167) (0.11653) (0.53900) (0.50285)
0.000000 1.000000 1.121425 0.428889 -3.783595 -15.19860
(0.27025) (0.22230) (1.02820) (0.95923)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.432464 -0.234951
(0.17872) (0.09488)
D(TOTALENER) 0.371622 -0.153268
(0.30765) (0.16333)
D(ELEC) 1.772272 -1.130601
(0.43780) (0.23243)
D(PETROL) 0.313840 -0.356207
(0.81162) (0.43088)
D(ENERPRICE) 0.622642 -0.134986
(0.42126) (0.22364)
3 Cointegrating Equation(s): Log likelihood 254.4701
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.000000 0.014757 -0.924165 -18.80287
(0.05044) (0.15251) (0.13719)
0.000000 1.000000 0.000000 -0.039260 -0.485291 -11.83083
(0.06704) (0.20268) (0.18233)
0.000000 0.000000 1.000000 0.417459 -2.941172 -3.003115
(0.11061) (0.33442) (0.30083)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.231105 0.046107 -0.138457
(0.17836) (0.14913) (0.04678)
D(TOTALENER) 0.750030 -0.681452 0.008078
(0.29687) (0.24822) (0.07787)
D(ELEC) 1.611113 -0.905655 -0.668200
(0.49878) (0.41703) (0.13082)
D(PETROL) 0.661129 -0.840955 -0.243839
(0.92012) (0.76933) (0.24134)
D(ENERPRICE) 0.562145 -0.050544 0.058797
(0.48555) (0.40597) (0.12736)
4 Cointegrating Equation(s): Log likelihood 265.5982
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.000000 0.000000 -1.019268 -18.83392
(0.07839) (0.31138)
0.000000 1.000000 0.000000 0.000000 -0.232279 -11.74824
(0.25215) (1.00156)
0.000000 0.000000 1.000000 0.000000 -5.631527 -3.881347
(2.43285) (9.66354)
0.000000 0.000000 0.000000 1.000000 6.444603 2.103758
(5.76254) (22.8894)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.211792 0.052076 -0.132147 -0.054017
(0.41262) (0.18832) (0.13025) (0.04589)
D(TOTALENER) 0.065111 -0.469746 0.231838 0.118582
(0.65824) (0.30042) (0.20778) (0.07320)
D(ELEC) 0.471966 -0.553549 -0.296044 -0.090905
(1.10691) (0.50519) (0.34941) (0.12310)
D(PETROL) 2.873431 -1.524769 -0.966589 -0.308984
(2.03236) (0.92756) (0.64154) (0.22602)
D(ENERPRICE) 3.229740 -0.875088 -0.812696 -0.266581
(0.82373) (0.37595) (0.26002) (0.09161)
Thanks in advance for your help!
I am currently conducting johansen tests for energy prices, energy consumption (total energy, electricy and oil) , gdp over 28 i determine the lag lenth trhough var lag order criteria (below eviexs output),
after that, I obtained the following johansen cointegration results. The Max-eigenvalue test indicates 4 cointegrating equation(s) at the 5% level and only 1 cointegrating equation(s) at the 1% level.
I am wondering if the high values for the trace and the max. eigenvalue are "normal" or if they are caused by some misspecification or wrong lag length. (below one eviews output)
why i obtained two differents results from the The Max-eigenvalue at 1% and 5%?
What results can i retain?
VAR Lag Order Selection Criteria
Endogenous variables: GDP TOTALENER ELEC PETROL ENERPRICE
Exogenous variables: C
Date: 07/20/10 Time: 03:38
Sample: 1980 2008
Included observations: 27
Lag LogL LR FPE AIC SC HQ
0 60.92141 NA 1.09E-08 -4.142327 -3.902357 -4.070971
1 189.2577 199.6342 5.38E-12 -11.79687 -10.35705* -11.36873
2 223.2814 40.32442* 3.41E-12* -12.46529* -9.825623 -11.68038*
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
Date: 07/20/10 Time: 04:22
Sample(adjusted): 1983 2008
Included observations: 26 after adjusting endpoints
Trend assumption: No deterministic trend (restricted constant)
Series: GDP TOTALENER ELEC PETROL ENERPRICE
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test
Hypothesized Trace 5 Percent 1 Percent
No. of CE(s) Eigenvalue Statistic Critical Value Critical Value
None ** 0.873969 133.8001 76.07 84.45
At most 1 ** 0.693950 79.94806 53.12 60.16
At most 2 ** 0.582673 49.16386 34.91 41.07
At most 3 ** 0.575145 26.44282 19.96 24.60
At most 4 0.148729 4.186644 9.24 12.97
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Trace test indicates 4 cointegrating equation(s) at both 5% and 1% levels
Hypothesized Max-Eigen 5 Percent 1 Percent
No. of CE(s) Eigenvalue Statistic Critical Value Critical Value
None ** 0.873969 53.85201 34.40 39.79
At most 1 * 0.693950 30.78420 28.14 33.24
At most 2 * 0.582673 22.72104 22.00 26.81
At most 3 ** 0.575145 22.25618 15.67 20.20
At most 4 0.148729 4.186644 9.24 12.97
*(**) denotes rejection of the hypothesis at the 5%(1%) level
Max-eigenvalue test indicates 4 cointegrating equation(s) at the 5% level
Max-eigenvalue test indicates 1 cointegrating equation(s) at the 1% level
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
GDP TOTALENER ELEC PETROL ENERPRICE C
-31.74070 16.53381 7.421725 1.980752 -0.518644 378.9193
3.968486 3.876127 5.737066 2.301376 -22.42228 -137.7058
-18.48685 25.80403 -2.431289 -2.300829 11.71328 49.62418
77.08022 -23.82520 -25.18183 -8.709145 12.65383 -1092.401
18.11751 9.239821 -7.139590 3.571202 -22.04718 -425.2288
Unrestricted Adjustment Coefficients (alpha):
D(GDP) -0.013829 -0.001629 0.010892 -0.000251 -0.005922
D(TOTALENER) -0.010860 0.006783 -0.020469 -0.008886 -0.008570
D(ELEC) -0.060199 -0.034900 0.008717 -0.014779 0.013580
D(PETROL) -0.013942 -0.032427 -0.018786 0.028701 -0.032557
D(ENERPRICE) -0.015633 0.031859 0.003272 0.034608 -0.001624
1 Cointegrating Equation(s): Log likelihood 227.7175
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 -0.520903 -0.233824 -0.062404 0.016340 -11.93796
(0.08487) (0.03424) (0.02399) (0.11421) (0.96212)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.438927
(0.17784)
D(TOTALENER) 0.344706
(0.31029)
D(ELEC) 1.910771
(0.52012)
D(PETROL) 0.442528
(0.84806)
D(ENERPRICE) 0.496209
(0.49285)
2 Cointegrating Equation(s): Log likelihood 243.1096
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.350330 0.161005 -1.954544 -19.85496
(0.14167) (0.11653) (0.53900) (0.50285)
0.000000 1.000000 1.121425 0.428889 -3.783595 -15.19860
(0.27025) (0.22230) (1.02820) (0.95923)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.432464 -0.234951
(0.17872) (0.09488)
D(TOTALENER) 0.371622 -0.153268
(0.30765) (0.16333)
D(ELEC) 1.772272 -1.130601
(0.43780) (0.23243)
D(PETROL) 0.313840 -0.356207
(0.81162) (0.43088)
D(ENERPRICE) 0.622642 -0.134986
(0.42126) (0.22364)
3 Cointegrating Equation(s): Log likelihood 254.4701
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.000000 0.014757 -0.924165 -18.80287
(0.05044) (0.15251) (0.13719)
0.000000 1.000000 0.000000 -0.039260 -0.485291 -11.83083
(0.06704) (0.20268) (0.18233)
0.000000 0.000000 1.000000 0.417459 -2.941172 -3.003115
(0.11061) (0.33442) (0.30083)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.231105 0.046107 -0.138457
(0.17836) (0.14913) (0.04678)
D(TOTALENER) 0.750030 -0.681452 0.008078
(0.29687) (0.24822) (0.07787)
D(ELEC) 1.611113 -0.905655 -0.668200
(0.49878) (0.41703) (0.13082)
D(PETROL) 0.661129 -0.840955 -0.243839
(0.92012) (0.76933) (0.24134)
D(ENERPRICE) 0.562145 -0.050544 0.058797
(0.48555) (0.40597) (0.12736)
4 Cointegrating Equation(s): Log likelihood 265.5982
Normalized cointegrating coefficients (std.err. in parentheses)
GDP TOTALENER ELEC PETROL ENERPRICE C
1.000000 0.000000 0.000000 0.000000 -1.019268 -18.83392
(0.07839) (0.31138)
0.000000 1.000000 0.000000 0.000000 -0.232279 -11.74824
(0.25215) (1.00156)
0.000000 0.000000 1.000000 0.000000 -5.631527 -3.881347
(2.43285) (9.66354)
0.000000 0.000000 0.000000 1.000000 6.444603 2.103758
(5.76254) (22.8894)
Adjustment coefficients (std.err. in parentheses)
D(GDP) 0.211792 0.052076 -0.132147 -0.054017
(0.41262) (0.18832) (0.13025) (0.04589)
D(TOTALENER) 0.065111 -0.469746 0.231838 0.118582
(0.65824) (0.30042) (0.20778) (0.07320)
D(ELEC) 0.471966 -0.553549 -0.296044 -0.090905
(1.10691) (0.50519) (0.34941) (0.12310)
D(PETROL) 2.873431 -1.524769 -0.966589 -0.308984
(2.03236) (0.92756) (0.64154) (0.22602)
D(ENERPRICE) 3.229740 -0.875088 -0.812696 -0.266581
(0.82373) (0.37595) (0.26002) (0.09161)
Thanks in advance for your help!