Alpha and Beta in Johansen cointegration
Posted: Thu Apr 23, 2009 8:16 am
hi can someone tell me
1) how to interpret alpha and beta coefficients (adjustment coefficient and cointegrating coefficient) of the Johansen method?
2) Where can one find these coefficient in the EViews result sheets? suppose the following is the Johansen result sheet where are the alpha and beta coefficients?
Date: 04/23/09 Time: 20:36
Sample (adjusted): 1952 2005
Included observations: 54 after adjustments
Trend assumption: Linear deterministic trend
Series: TB ER GDP GWP
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.473511 69.80137 47.85613 0.0001
At most 1 * 0.360043 35.15906 29.79707 0.0110
At most 2 0.185139 11.05596 15.49471 0.2081
At most 3 1.67E-06 9.00E-05 3.841466 0.9937
Trace test indicates 2 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.473511 34.64232 27.58434 0.0053
At most 1 * 0.360043 24.10310 21.13162 0.0185
At most 2 0.185139 11.05587 14.26460 0.1514
At most 3 1.67E-06 9.00E-05 3.841466 0.9937
Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
TB ER GDP GWP
-0.005653 30.18754 -0.000374 2.01E-13
0.004336 5.581128 0.000190 2.07E-13
-0.003253 43.61279 -0.001238 5.66E-13
-0.000419 26.53447 0.000128 5.16E-14
Unrestricted Adjustment Coefficients (alpha):
D(TB) 18.28180 -66.78197 -4.523459 -0.153296
D(ER) 0.000868 -0.002472 -0.002513 5.22E-06
D(GDP) 217.0575 -60.35638 59.13545 0.395793
D(GWP) 1.98E+11 1.18E+11 -3.17E+10 -1.48E+08
1 Cointegrating Equation(s): Log likelihood -2070.782 -------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 -5339.735 0.066170 -3.56E-11
(1231.01) (0.02622) (1.6E-11)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.103354
(0.13401)
D(ER) -4.91E-06
(6.7E-06)
D(GDP) -1.227108
(0.34175)
D(GWP) -1.12E+09
(2.6E+08)
2 Cointegrating Equation(s): Log likelihood -2058.731 --------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 0.000000 0.048193 3.16E-11
(0.02789) (1.0E-11)
0.000000 1.000000 -3.37E-06 1.26E-14
(6.0E-06) (2.2E-15)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.392920 179.1637
(0.15429) (664.827)
D(ER) -1.56E-05 0.012412
(8.1E-06) (0.03493)
D(GDP) -1.488813 6215.574
(0.42619) (1836.38)
D(GWP) -6.08E+08 6.64E+12
(3.0E+08) (1.3E+12)
3 Cointegrating Equation(s): Log likelihood -2053.203 --------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 0.000000 0.000000 3.78E-11
(4.5E-12)
0.000000 1.000000 0.000000 1.21E-14
(1.2E-15)
0.000000 0.000000 1.000000 -1.29E-10
(5.6E-11)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.378205 -18.11697 -0.013938
(0.16954) (1154.49) (0.02830)
D(ER) -7.45E-06 -0.097195 2.32E-06
(8.4E-06) (0.05752) (1.4E-06)
D(GDP) -1.681191 8794.636 -0.165905
(0.46372) (3157.73) (0.07741)
D(GWP) -5.05E+08 5.25E+12 -12384030
(3.3E+08) (2.3E+12) (5.5E+07)
1) how to interpret alpha and beta coefficients (adjustment coefficient and cointegrating coefficient) of the Johansen method?
2) Where can one find these coefficient in the EViews result sheets? suppose the following is the Johansen result sheet where are the alpha and beta coefficients?
Date: 04/23/09 Time: 20:36
Sample (adjusted): 1952 2005
Included observations: 54 after adjustments
Trend assumption: Linear deterministic trend
Series: TB ER GDP GWP
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.473511 69.80137 47.85613 0.0001
At most 1 * 0.360043 35.15906 29.79707 0.0110
At most 2 0.185139 11.05596 15.49471 0.2081
At most 3 1.67E-06 9.00E-05 3.841466 0.9937
Trace test indicates 2 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.473511 34.64232 27.58434 0.0053
At most 1 * 0.360043 24.10310 21.13162 0.0185
At most 2 0.185139 11.05587 14.26460 0.1514
At most 3 1.67E-06 9.00E-05 3.841466 0.9937
Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
TB ER GDP GWP
-0.005653 30.18754 -0.000374 2.01E-13
0.004336 5.581128 0.000190 2.07E-13
-0.003253 43.61279 -0.001238 5.66E-13
-0.000419 26.53447 0.000128 5.16E-14
Unrestricted Adjustment Coefficients (alpha):
D(TB) 18.28180 -66.78197 -4.523459 -0.153296
D(ER) 0.000868 -0.002472 -0.002513 5.22E-06
D(GDP) 217.0575 -60.35638 59.13545 0.395793
D(GWP) 1.98E+11 1.18E+11 -3.17E+10 -1.48E+08
1 Cointegrating Equation(s): Log likelihood -2070.782 -------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 -5339.735 0.066170 -3.56E-11
(1231.01) (0.02622) (1.6E-11)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.103354
(0.13401)
D(ER) -4.91E-06
(6.7E-06)
D(GDP) -1.227108
(0.34175)
D(GWP) -1.12E+09
(2.6E+08)
2 Cointegrating Equation(s): Log likelihood -2058.731 --------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 0.000000 0.048193 3.16E-11
(0.02789) (1.0E-11)
0.000000 1.000000 -3.37E-06 1.26E-14
(6.0E-06) (2.2E-15)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.392920 179.1637
(0.15429) (664.827)
D(ER) -1.56E-05 0.012412
(8.1E-06) (0.03493)
D(GDP) -1.488813 6215.574
(0.42619) (1836.38)
D(GWP) -6.08E+08 6.64E+12
(3.0E+08) (1.3E+12)
3 Cointegrating Equation(s): Log likelihood -2053.203 --------------------------------------------------what does these mean?
Normalized cointegrating coefficients (standard error in parentheses)
TB ER GDP GWP
1.000000 0.000000 0.000000 3.78E-11
(4.5E-12)
0.000000 1.000000 0.000000 1.21E-14
(1.2E-15)
0.000000 0.000000 1.000000 -1.29E-10
(5.6E-11)
Adjustment coefficients (standard error in parentheses)
D(TB) -0.378205 -18.11697 -0.013938
(0.16954) (1154.49) (0.02830)
D(ER) -7.45E-06 -0.097195 2.32E-06
(8.4E-06) (0.05752) (1.4E-06)
D(GDP) -1.681191 8794.636 -0.165905
(0.46372) (3157.73) (0.07741)
D(GWP) -5.05E+08 5.25E+12 -12384030
(3.3E+08) (2.3E+12) (5.5E+07)