Interest Rate Spread and DG10 Model
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This assignment investigates the impact of interest rate spreads on the DG10 model using econometric analysis. It starts by building a regression model including various explanatory variables and then refines it by removing insignificant variables. The final model focuses on the statistically significant variables, G10t-1 (previous period DG10) and SPREADt-1 (previous period interest rate spread), to determine their influence on the current DG10 value. The speed of adjustment is calculated based on the coefficient of the SPREADt-1 variable.
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Running Head: FINANCE WITH EVIEWS
Finance with Eviews
Name of the Student
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Finance with Eviews
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Author note
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Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................3
Martingale test.............................................................................................................................4
Answer 3..........................................................................................................................................6
Answer 4........................................................................................................................................16
Order of integration for SPREAD.............................................................................................16
Co-integration test.....................................................................................................................22
Answer 5........................................................................................................................................27
Error Correction Model.............................................................................................................27
FINANCE WITH EVIEWS
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................3
Martingale test.............................................................................................................................4
Answer 3..........................................................................................................................................6
Answer 4........................................................................................................................................16
Order of integration for SPREAD.............................................................................................16
Co-integration test.....................................................................................................................22
Answer 5........................................................................................................................................27
Error Correction Model.............................................................................................................27
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Answer 1
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G10
The above graph shows the movement of series G10. The variable first moves upward.
After reaching peak point it finally constitutes a downward trend with significant fluctuation in
the movement.
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TB3MS
Like G10, the variable TB3MS shows a fluctuating trend with first going upwards and
finally ends at a significantly low level.
FINANCE WITH EVIEWS
Answer 1
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G10
The above graph shows the movement of series G10. The variable first moves upward.
After reaching peak point it finally constitutes a downward trend with significant fluctuation in
the movement.
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60 65 70 75 80 85 90 95 00 05 10
TB3MS
Like G10, the variable TB3MS shows a fluctuating trend with first going upwards and
finally ends at a significantly low level.
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FINANCE WITH EVIEWS
Answer 2
To test whether the variable G10 is martingale or random walk first a regression of the
variable is run only on constant and then a ARCH test of residual is conducted.
Regression equation on Constant
Dependent Variable: G10
Method: Least Squares
Date: 01/06/18 Time: 20:00
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 6.321798 0.180301 35.06254 0.0000
R-squared 0.000000 Mean dependent var 6.321798
Adjusted R-squared 0.000000 S.D. dependent var 2.722480
S.E. of regression 2.722480 Akaike info criterion 4.845340
Sum squared resid 1682.500 Schwarz criterion 4.860381
Log likelihood -551.3687 Hannan-Quinn criter. 4.851408
Durbin-Watson stat 0.030447
ARCH test of Residuals
Heteroskedasticity Test: ARCH
F-statistic 1908.910 Prob. F(1,225) 0.0000
Obs*R-squared 203.0651 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 01/06/18 Time: 20:23
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.414295 0.301315 1.374956 0.1705
RESID^2(-1) 0.946230 0.021657 43.69108 0.0000
R-squared 0.894560 Mean dependent var 7.374374
Adjusted R-squared 0.894091 S.D. dependent var 11.84078
S.E. of regression 3.853420 Akaike info criterion 5.544571
Sum squared resid 3340.990 Schwarz criterion 5.574746
Log likelihood -627.3088 Hannan-Quinn criter. 5.556747
FINANCE WITH EVIEWS
Answer 2
To test whether the variable G10 is martingale or random walk first a regression of the
variable is run only on constant and then a ARCH test of residual is conducted.
Regression equation on Constant
Dependent Variable: G10
Method: Least Squares
Date: 01/06/18 Time: 20:00
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 6.321798 0.180301 35.06254 0.0000
R-squared 0.000000 Mean dependent var 6.321798
Adjusted R-squared 0.000000 S.D. dependent var 2.722480
S.E. of regression 2.722480 Akaike info criterion 4.845340
Sum squared resid 1682.500 Schwarz criterion 4.860381
Log likelihood -551.3687 Hannan-Quinn criter. 4.851408
Durbin-Watson stat 0.030447
ARCH test of Residuals
Heteroskedasticity Test: ARCH
F-statistic 1908.910 Prob. F(1,225) 0.0000
Obs*R-squared 203.0651 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 01/06/18 Time: 20:23
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.414295 0.301315 1.374956 0.1705
RESID^2(-1) 0.946230 0.021657 43.69108 0.0000
R-squared 0.894560 Mean dependent var 7.374374
Adjusted R-squared 0.894091 S.D. dependent var 11.84078
S.E. of regression 3.853420 Akaike info criterion 5.544571
Sum squared resid 3340.990 Schwarz criterion 5.574746
Log likelihood -627.3088 Hannan-Quinn criter. 5.556747
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F-statistic 1908.910 Durbin-Watson stat 1.563370
Prob(F-statistic) 0.000000
The p value of the ARCH test statistics is less than the value of significance level. This
indicates rejection of the null hypothesis stating the absence of auto regressive heteroskadasticy.
Henceforth, the hypothesis of whether G10 is martingale is tested.
Martingale test
In order to test whether the variable G10 is a Martingale two tests have been selected –
the Chow-Detming test and Kim’s wild bootstrap test. The former is an asymptotic test.
Although, in terms of test statistics both the tests provide same result, but their P value differ
significantly. Unlike, Chow-Denning test Wild Bootstrap test does not rely on asymptotic values.
Chow- Denning test
Null Hypothesis: G10 is a martingale
Date: 01/05/18 Time: 12:19
Sample: 1957Q1 2013Q4
Included observations: 227 (after adjustments)
Heteroskedasticity robust standard error estimates
User-specified lags: 2 4 8 16
Joint Tests Value df Probability
Max |z| (at period 2)* 2.690008 227 0.0283
Individual Tests
Period Var. Ratio Std. Error z-Statistic Probability
2 1.250117 0.092980 2.690008 0.0071
4 1.393742 0.171192 2.300002 0.0214
8 1.336163 0.270971 1.240590 0.2148
16 1.290815 0.405342 0.717454 0.4731
*Probability approximation using studentized maximum modulus with
parameter value 4 and infinite degrees of freedom
Test Details (Mean = -0.00289280469897)
Period Variance Var. Ratio Obs.
1 0.22666 -- 227
2 0.28335 1.25012 226
4 0.31591 1.39374 224
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F-statistic 1908.910 Durbin-Watson stat 1.563370
Prob(F-statistic) 0.000000
The p value of the ARCH test statistics is less than the value of significance level. This
indicates rejection of the null hypothesis stating the absence of auto regressive heteroskadasticy.
Henceforth, the hypothesis of whether G10 is martingale is tested.
Martingale test
In order to test whether the variable G10 is a Martingale two tests have been selected –
the Chow-Detming test and Kim’s wild bootstrap test. The former is an asymptotic test.
Although, in terms of test statistics both the tests provide same result, but their P value differ
significantly. Unlike, Chow-Denning test Wild Bootstrap test does not rely on asymptotic values.
Chow- Denning test
Null Hypothesis: G10 is a martingale
Date: 01/05/18 Time: 12:19
Sample: 1957Q1 2013Q4
Included observations: 227 (after adjustments)
Heteroskedasticity robust standard error estimates
User-specified lags: 2 4 8 16
Joint Tests Value df Probability
Max |z| (at period 2)* 2.690008 227 0.0283
Individual Tests
Period Var. Ratio Std. Error z-Statistic Probability
2 1.250117 0.092980 2.690008 0.0071
4 1.393742 0.171192 2.300002 0.0214
8 1.336163 0.270971 1.240590 0.2148
16 1.290815 0.405342 0.717454 0.4731
*Probability approximation using studentized maximum modulus with
parameter value 4 and infinite degrees of freedom
Test Details (Mean = -0.00289280469897)
Period Variance Var. Ratio Obs.
1 0.22666 -- 227
2 0.28335 1.25012 226
4 0.31591 1.39374 224
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8 0.30286 1.33616 220
16 0.29258 1.29081 212
Wild Bootstrap test
Null Hypothesis: G10 is a martingale
Date: 01/05/18 Time: 12:20
Sample: 1957Q1 2013Q4
Included observations: 227 (after adjustments)
Heteroskedasticity robust standard error estimates
User-specified lags: 2 4 8 16
Test probabilities computed using wild bootstrap: dist=twopoint,
reps=1000, rng=kn, seed=1964920415
Joint Tests Value df Probability
Max |z| (at period 2) 2.690008 227 0.0410
Individual Tests
Period Var. Ratio Std. Error z-Statistic Probability
2 1.250117 0.092980 2.690008 0.0020
4 1.393742 0.171192 2.300002 0.0230
8 1.336163 0.270971 1.240590 0.2170
16 1.290815 0.405342 0.717454 0.4970
Test Details (Mean = -0.00289280469897)
Period Variance Var. Ratio Obs.
1 0.22666 -- 227
2 0.28335 1.25012 226
4 0.31591 1.39374 224
8 0.30286 1.33616 220
16 0.29258 1.29081 212
Both the tests have a same value of test statistics with the value being 2.69008. The P value for
Chow-Denning test is obtained as 0.0283. The same for Wild bootstrap test is 0.0410. Both the p
values are less than 5% significance level. Therefore, the null hypothesis that G10 is a random
walk or martingale is rejected. Hence, G10 is not a random walk or martingale.
Answer 3
The decision regarding order of integration is taken by examining the graph of the variable, it
correlogram and finally Augmented Dickey Fuller test.
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8 0.30286 1.33616 220
16 0.29258 1.29081 212
Wild Bootstrap test
Null Hypothesis: G10 is a martingale
Date: 01/05/18 Time: 12:20
Sample: 1957Q1 2013Q4
Included observations: 227 (after adjustments)
Heteroskedasticity robust standard error estimates
User-specified lags: 2 4 8 16
Test probabilities computed using wild bootstrap: dist=twopoint,
reps=1000, rng=kn, seed=1964920415
Joint Tests Value df Probability
Max |z| (at period 2) 2.690008 227 0.0410
Individual Tests
Period Var. Ratio Std. Error z-Statistic Probability
2 1.250117 0.092980 2.690008 0.0020
4 1.393742 0.171192 2.300002 0.0230
8 1.336163 0.270971 1.240590 0.2170
16 1.290815 0.405342 0.717454 0.4970
Test Details (Mean = -0.00289280469897)
Period Variance Var. Ratio Obs.
1 0.22666 -- 227
2 0.28335 1.25012 226
4 0.31591 1.39374 224
8 0.30286 1.33616 220
16 0.29258 1.29081 212
Both the tests have a same value of test statistics with the value being 2.69008. The P value for
Chow-Denning test is obtained as 0.0283. The same for Wild bootstrap test is 0.0410. Both the p
values are less than 5% significance level. Therefore, the null hypothesis that G10 is a random
walk or martingale is rejected. Hence, G10 is not a random walk or martingale.
Answer 3
The decision regarding order of integration is taken by examining the graph of the variable, it
correlogram and finally Augmented Dickey Fuller test.
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FINANCE WITH EVIEWS
Order of integration
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G10
The variable G10 first moves upward. After reaching peak point it finally constitutes a
downward trend with significant fluctuation in the movement.
Correlogram
Correlogram provides a test of autocorrelation and partial auto correlation at different lag
values.
FINANCE WITH EVIEWS
Order of integration
0
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60 65 70 75 80 85 90 95 00 05 10
G10
The variable G10 first moves upward. After reaching peak point it finally constitutes a
downward trend with significant fluctuation in the movement.
Correlogram
Correlogram provides a test of autocorrelation and partial auto correlation at different lag
values.
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From the correlogram, it is seen that there is gradual decline in the autocorrelation series.
Moreover, Q statistics for Ljung-Box test produce a statistically significant result. The null
hypothesis that autocorrelations taken up to a particular order are zero. From the result, the non-
stationarity of the variable G10 is clearly evidenced.
FINANCE WITH EVIEWS
From the correlogram, it is seen that there is gradual decline in the autocorrelation series.
Moreover, Q statistics for Ljung-Box test produce a statistically significant result. The null
hypothesis that autocorrelations taken up to a particular order are zero. From the result, the non-
stationarity of the variable G10 is clearly evidenced.
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ADF test
The non-stationarity of the variable is further confirmed with testing the presence of unit
root using Augmented Dickey Fuller test. The null hypothesis of ADF test is that the series
contain a unit root. ADF test is first performed at level.
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.760022 0.7209
Test critical values: 1% level -3.999180
5% level -3.429834
10% level -3.138449
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:12
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.020220 0.011488 -1.760022 0.0798
D(G10(-1)) 0.240723 0.065055 3.700318 0.0003
C 0.203320 0.101886 1.995560 0.0472
@TREND(1957Q1) -0.000682 0.000478 -1.426729 0.1551
R-squared 0.076271 Mean dependent var -0.003894
Adjusted R-squared 0.063788 S.D. dependent var 0.476907
S.E. of regression 0.461446 Akaike info criterion 1.308636
Sum squared resid 47.27095 Schwarz criterion 1.369177
Log likelihood -143.8759 Hannan-Quinn criter. 1.333068
F-statistic 6.110061 Durbin-Watson stat 1.951654
Prob(F-statistic) 0.000519
Null hypothesis that the series G(10) is I(1) is not rejected as the t computed t value -
1.448648 is greater than critical value of -3.429745.
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ADF test
The non-stationarity of the variable is further confirmed with testing the presence of unit
root using Augmented Dickey Fuller test. The null hypothesis of ADF test is that the series
contain a unit root. ADF test is first performed at level.
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.760022 0.7209
Test critical values: 1% level -3.999180
5% level -3.429834
10% level -3.138449
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:12
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.020220 0.011488 -1.760022 0.0798
D(G10(-1)) 0.240723 0.065055 3.700318 0.0003
C 0.203320 0.101886 1.995560 0.0472
@TREND(1957Q1) -0.000682 0.000478 -1.426729 0.1551
R-squared 0.076271 Mean dependent var -0.003894
Adjusted R-squared 0.063788 S.D. dependent var 0.476907
S.E. of regression 0.461446 Akaike info criterion 1.308636
Sum squared resid 47.27095 Schwarz criterion 1.369177
Log likelihood -143.8759 Hannan-Quinn criter. 1.333068
F-statistic 6.110061 Durbin-Watson stat 1.951654
Prob(F-statistic) 0.000519
Null hypothesis that the series G(10) is I(1) is not rejected as the t computed t value -
1.448648 is greater than critical value of -3.429745.
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The trend co-efficient is not significantly different from zero. Therefore, this is not a
trended series. The constant term is statistically significant.
The equation is re estimated using trend component.
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:16
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.203320 0.101886 1.995560 0.0472
G10(-1) -0.020220 0.011488 -1.760022 0.0798
D(G10(-1)) 0.240723 0.065055 3.700318 0.0003
@TREND -0.000682 0.000478 -1.426729 0.1551
R-squared 0.076271 Mean dependent var -0.003894
Adjusted R-squared 0.063788 S.D. dependent var 0.476907
S.E. of regression 0.461446 Akaike info criterion 1.308636
Sum squared resid 47.27095 Schwarz criterion 1.369177
Log likelihood -143.8759 Hannan-Quinn criter. 1.333068
F-statistic 6.110061 Durbin-Watson stat 1.951654
Prob(F-statistic) 0.000519
Autocorrelation test
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 3.334479 Prob. F(2,220) 0.0374
Obs*R-squared 6.649275 Prob. Chi-Square(2) 0.0360
The null hypothesis that the there is no first order auto correlation is rejected. This means the
residual are auto-correlated
Heteroscadasticity test
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 15.23974 Prob. F(3,222) 0.0000
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The trend co-efficient is not significantly different from zero. Therefore, this is not a
trended series. The constant term is statistically significant.
The equation is re estimated using trend component.
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:16
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.203320 0.101886 1.995560 0.0472
G10(-1) -0.020220 0.011488 -1.760022 0.0798
D(G10(-1)) 0.240723 0.065055 3.700318 0.0003
@TREND -0.000682 0.000478 -1.426729 0.1551
R-squared 0.076271 Mean dependent var -0.003894
Adjusted R-squared 0.063788 S.D. dependent var 0.476907
S.E. of regression 0.461446 Akaike info criterion 1.308636
Sum squared resid 47.27095 Schwarz criterion 1.369177
Log likelihood -143.8759 Hannan-Quinn criter. 1.333068
F-statistic 6.110061 Durbin-Watson stat 1.951654
Prob(F-statistic) 0.000519
Autocorrelation test
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 3.334479 Prob. F(2,220) 0.0374
Obs*R-squared 6.649275 Prob. Chi-Square(2) 0.0360
The null hypothesis that the there is no first order auto correlation is rejected. This means the
residual are auto-correlated
Heteroscadasticity test
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 15.23974 Prob. F(3,222) 0.0000
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Obs*R-squared 38.59471 Prob. Chi-Square(3) 0.0000
Scaled explained SS 94.35754 Prob. Chi-Square(3) 0.0000
Breusch-Pagan-Godfrey rejects the null hypothesis that the disturbances are homscadastic.
MAIC
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 7 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.223850 0.9025
Test critical values: 1% level -4.000316
5% level -3.430383
10% level -3.138772
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:23
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.014617 0.011944 -1.223850 0.2224
D(G10(-1)) 0.262266 0.068017 3.855894 0.0002
D(G10(-2)) -0.140945 0.070720 -1.993009 0.0476
D(G10(-3)) 0.132813 0.070138 1.893604 0.0597
D(G10(-4)) -0.006738 0.070736 -0.095261 0.9242
D(G10(-5)) -0.180765 0.070263 -2.572677 0.0108
D(G10(-6)) 0.028863 0.070309 0.410515 0.6818
D(G10(-7)) -0.154146 0.068100 -2.263533 0.0246
C 0.204219 0.107449 1.900606 0.0587
@TREND(1957Q1) -0.000993 0.000503 -1.973255 0.0498
R-squared 0.151898 Mean dependent var -0.004788
Adjusted R-squared 0.115550 S.D. dependent var 0.478812
S.E. of regression 0.450300 Akaike info criterion 1.286583
Sum squared resid 42.58167 Schwarz criterion 1.440838
Log likelihood -131.5241 Hannan-Quinn criter. 1.348875
F-statistic 4.179072 Durbin-Watson stat 1.978275
Prob(F-statistic) 0.000056
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Obs*R-squared 38.59471 Prob. Chi-Square(3) 0.0000
Scaled explained SS 94.35754 Prob. Chi-Square(3) 0.0000
Breusch-Pagan-Godfrey rejects the null hypothesis that the disturbances are homscadastic.
MAIC
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 7 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.223850 0.9025
Test critical values: 1% level -4.000316
5% level -3.430383
10% level -3.138772
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:23
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.014617 0.011944 -1.223850 0.2224
D(G10(-1)) 0.262266 0.068017 3.855894 0.0002
D(G10(-2)) -0.140945 0.070720 -1.993009 0.0476
D(G10(-3)) 0.132813 0.070138 1.893604 0.0597
D(G10(-4)) -0.006738 0.070736 -0.095261 0.9242
D(G10(-5)) -0.180765 0.070263 -2.572677 0.0108
D(G10(-6)) 0.028863 0.070309 0.410515 0.6818
D(G10(-7)) -0.154146 0.068100 -2.263533 0.0246
C 0.204219 0.107449 1.900606 0.0587
@TREND(1957Q1) -0.000993 0.000503 -1.973255 0.0498
R-squared 0.151898 Mean dependent var -0.004788
Adjusted R-squared 0.115550 S.D. dependent var 0.478812
S.E. of regression 0.450300 Akaike info criterion 1.286583
Sum squared resid 42.58167 Schwarz criterion 1.440838
Log likelihood -131.5241 Hannan-Quinn criter. 1.348875
F-statistic 4.179072 Durbin-Watson stat 1.978275
Prob(F-statistic) 0.000056
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Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:25
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.204219 0.107449 1.900606 0.0587
G10(-1) -0.014617 0.011944 -1.223850 0.2224
D(G10(-1)) 0.262266 0.068017 3.855894 0.0002
D(G10(-2)) -0.140945 0.070720 -1.993009 0.0476
D(G10(-3)) 0.132813 0.070138 1.893604 0.0597
D(G10(-4)) -0.006738 0.070736 -0.095261 0.9242
D(G10(-5)) -0.180765 0.070263 -2.572677 0.0108
D(G10(-6)) 0.028863 0.070309 0.410515 0.6818
D(G10(-7)) -0.154146 0.068100 -2.263533 0.0246
@TREND -0.000993 0.000503 -1.973255 0.0498
R-squared 0.151898 Mean dependent var -0.004788
Adjusted R-squared 0.115550 S.D. dependent var 0.478812
S.E. of regression 0.450300 Akaike info criterion 1.286583
Sum squared resid 42.58167 Schwarz criterion 1.440838
Log likelihood -131.5241 Hannan-Quinn criter. 1.348875
F-statistic 4.179072 Durbin-Watson stat 1.978275
Prob(F-statistic) 0.000056
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.557354 Prob. F(2,208) 0.5736
Obs*R-squared 1.172733 Prob. Chi-Square(2) 0.5563
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 6.438922 Prob. F(9,210) 0.0000
Obs*R-squared 47.57996 Prob. Chi-Square(9) 0.0000
Scaled explained SS 98.80355 Prob. Chi-Square(9) 0.0000
With modified information criterion, the series still remains heteroscadastic.
Next, Phillips- Perron test is performed
Phillips-Perron test
FINANCE WITH EVIEWS
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:25
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.204219 0.107449 1.900606 0.0587
G10(-1) -0.014617 0.011944 -1.223850 0.2224
D(G10(-1)) 0.262266 0.068017 3.855894 0.0002
D(G10(-2)) -0.140945 0.070720 -1.993009 0.0476
D(G10(-3)) 0.132813 0.070138 1.893604 0.0597
D(G10(-4)) -0.006738 0.070736 -0.095261 0.9242
D(G10(-5)) -0.180765 0.070263 -2.572677 0.0108
D(G10(-6)) 0.028863 0.070309 0.410515 0.6818
D(G10(-7)) -0.154146 0.068100 -2.263533 0.0246
@TREND -0.000993 0.000503 -1.973255 0.0498
R-squared 0.151898 Mean dependent var -0.004788
Adjusted R-squared 0.115550 S.D. dependent var 0.478812
S.E. of regression 0.450300 Akaike info criterion 1.286583
Sum squared resid 42.58167 Schwarz criterion 1.440838
Log likelihood -131.5241 Hannan-Quinn criter. 1.348875
F-statistic 4.179072 Durbin-Watson stat 1.978275
Prob(F-statistic) 0.000056
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.557354 Prob. F(2,208) 0.5736
Obs*R-squared 1.172733 Prob. Chi-Square(2) 0.5563
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 6.438922 Prob. F(9,210) 0.0000
Obs*R-squared 47.57996 Prob. Chi-Square(9) 0.0000
Scaled explained SS 98.80355 Prob. Chi-Square(9) 0.0000
With modified information criterion, the series still remains heteroscadastic.
Next, Phillips- Perron test is performed
Phillips-Perron test
12
FINANCE WITH EVIEWS
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 4 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -1.667996 0.7623
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.221115
HAC corrected variance (Bartlett kernel) 0.308599
Phillips-Perron Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:27
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.016948 0.011699 -1.448648 0.1488
C 0.202251 0.103312 1.957667 0.0515
@TREND(1957Q1) -0.000857 0.000484 -1.770616 0.0780
R-squared 0.020155 Mean dependent var -0.002893
Adjusted R-squared 0.011406 S.D. dependent var 0.476090
S.E. of regression 0.473367 Akaike info criterion 1.355234
Sum squared resid 50.19300 Schwarz criterion 1.400498
Log likelihood -150.8191 Hannan-Quinn criter. 1.373499
F-statistic 2.303781 Durbin-Watson stat 1.524982
Prob(F-statistic) 0.102243
The Phillips-Perron test confirms that ADF result that the series is I(1) and both trend and
constant are not statistically significant.
So, ADF and Phillips Perron test is run with no constant and no trend.
Null Hypothesis: G10 has a unit root
Exogenous: None
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
FINANCE WITH EVIEWS
Null Hypothesis: G10 has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 4 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -1.667996 0.7623
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.221115
HAC corrected variance (Bartlett kernel) 0.308599
Phillips-Perron Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:27
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.016948 0.011699 -1.448648 0.1488
C 0.202251 0.103312 1.957667 0.0515
@TREND(1957Q1) -0.000857 0.000484 -1.770616 0.0780
R-squared 0.020155 Mean dependent var -0.002893
Adjusted R-squared 0.011406 S.D. dependent var 0.476090
S.E. of regression 0.473367 Akaike info criterion 1.355234
Sum squared resid 50.19300 Schwarz criterion 1.400498
Log likelihood -150.8191 Hannan-Quinn criter. 1.373499
F-statistic 2.303781 Durbin-Watson stat 1.524982
Prob(F-statistic) 0.102243
The Phillips-Perron test confirms that ADF result that the series is I(1) and both trend and
constant are not statistically significant.
So, ADF and Phillips Perron test is run with no constant and no trend.
Null Hypothesis: G10 has a unit root
Exogenous: None
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
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FINANCE WITH EVIEWS
Augmented Dickey-Fuller test statistic -0.707471 0.4094
Test critical values: 1% level -2.575234
5% level -1.942236
10% level -1.615764
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:31
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.003161 0.004468 -0.707471 0.4800
D(G10(-1)) 0.241117 0.064795 3.721201 0.0003
R-squared 0.059533 Mean dependent var -0.003894
Adjusted R-squared 0.055335 S.D. dependent var 0.476907
S.E. of regression 0.463524 Akaike info criterion 1.308895
Sum squared resid 48.12748 Schwarz criterion 1.339165
Log likelihood -145.9051 Hannan-Quinn criter. 1.321110
Durbin-Watson stat 1.951478
The ADF test with no constant no trend again fail to reject the null hypothesis that the
series is I(1).
Null Hypothesis: G10 has a unit root
Exogenous: None
Lag Length: 7 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.546848 0.4793
Test critical values: 1% level -2.575516
5% level -1.942276
10% level -1.615738
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:41
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
FINANCE WITH EVIEWS
Augmented Dickey-Fuller test statistic -0.707471 0.4094
Test critical values: 1% level -2.575234
5% level -1.942236
10% level -1.615764
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:31
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.003161 0.004468 -0.707471 0.4800
D(G10(-1)) 0.241117 0.064795 3.721201 0.0003
R-squared 0.059533 Mean dependent var -0.003894
Adjusted R-squared 0.055335 S.D. dependent var 0.476907
S.E. of regression 0.463524 Akaike info criterion 1.308895
Sum squared resid 48.12748 Schwarz criterion 1.339165
Log likelihood -145.9051 Hannan-Quinn criter. 1.321110
Durbin-Watson stat 1.951478
The ADF test with no constant no trend again fail to reject the null hypothesis that the
series is I(1).
Null Hypothesis: G10 has a unit root
Exogenous: None
Lag Length: 7 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.546848 0.4793
Test critical values: 1% level -2.575516
5% level -1.942276
10% level -1.615738
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:41
Sample (adjusted): 1959Q1 2013Q4
Included observations: 220 after adjustments
14
FINANCE WITH EVIEWS
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.002405 0.004398 -0.546848 0.5851
D(G10(-1)) 0.270194 0.067891 3.979831 0.0001
D(G10(-2)) -0.135607 0.070529 -1.922718 0.0559
D(G10(-3)) 0.138266 0.070161 1.970700 0.0501
D(G10(-4)) -0.005229 0.070735 -0.073923 0.9411
D(G10(-5)) -0.178546 0.070098 -2.547105 0.0116
D(G10(-6)) 0.033998 0.070322 0.483464 0.6293
D(G10(-7)) -0.145668 0.067704 -2.151549 0.0326
R-squared 0.133430 Mean dependent var -0.004788
Adjusted R-squared 0.104816 S.D. dependent var 0.478812
S.E. of regression 0.453024 Akaike info criterion 1.289943
Sum squared resid 43.50892 Schwarz criterion 1.413347
Log likelihood -133.8937 Hannan-Quinn criter. 1.339777
Durbin-Watson stat 1.977248
The result of ADF test is further supported by ADF based on the modified information criterion.
Null Hypothesis: G10 has a unit root
Exogenous: None
Bandwidth: 4 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -0.650700 0.4345
Test critical values: 1% level -2.575189
5% level -1.942230
10% level -1.615768
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.225359
HAC corrected variance (Bartlett kernel) 0.318444
Phillips-Perron Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:43
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.002562 0.004581 -0.559216 0.5766
R-squared 0.001345 Mean dependent var -0.002893
Adjusted R-squared 0.001345 S.D. dependent var 0.476090
S.E. of regression 0.475769 Akaike info criterion 1.356628
Sum squared resid 51.15656 Schwarz criterion 1.371716
FINANCE WITH EVIEWS
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.002405 0.004398 -0.546848 0.5851
D(G10(-1)) 0.270194 0.067891 3.979831 0.0001
D(G10(-2)) -0.135607 0.070529 -1.922718 0.0559
D(G10(-3)) 0.138266 0.070161 1.970700 0.0501
D(G10(-4)) -0.005229 0.070735 -0.073923 0.9411
D(G10(-5)) -0.178546 0.070098 -2.547105 0.0116
D(G10(-6)) 0.033998 0.070322 0.483464 0.6293
D(G10(-7)) -0.145668 0.067704 -2.151549 0.0326
R-squared 0.133430 Mean dependent var -0.004788
Adjusted R-squared 0.104816 S.D. dependent var 0.478812
S.E. of regression 0.453024 Akaike info criterion 1.289943
Sum squared resid 43.50892 Schwarz criterion 1.413347
Log likelihood -133.8937 Hannan-Quinn criter. 1.339777
Durbin-Watson stat 1.977248
The result of ADF test is further supported by ADF based on the modified information criterion.
Null Hypothesis: G10 has a unit root
Exogenous: None
Bandwidth: 4 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -0.650700 0.4345
Test critical values: 1% level -2.575189
5% level -1.942230
10% level -1.615768
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.225359
HAC corrected variance (Bartlett kernel) 0.318444
Phillips-Perron Test Equation
Dependent Variable: D(G10)
Method: Least Squares
Date: 01/08/18 Time: 08:43
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
G10(-1) -0.002562 0.004581 -0.559216 0.5766
R-squared 0.001345 Mean dependent var -0.002893
Adjusted R-squared 0.001345 S.D. dependent var 0.476090
S.E. of regression 0.475769 Akaike info criterion 1.356628
Sum squared resid 51.15656 Schwarz criterion 1.371716
15
FINANCE WITH EVIEWS
Log likelihood -152.9773 Hannan-Quinn criter. 1.362716
Durbin-Watson stat 1.517887
The Computed t value is greater than the critical value. Therefore, the null hypothesis that the
series contain unit root is accepted implying G10 is not stationary at level.
Now, the result can be further supported by KPSS test.
Null Hypothesis: G10 is stationary
Exogenous: Constant, Linear Trend
Bandwidth: 11 (Newey-West automatic) using Bartlett kernel
LM-Stat.
Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.437056
Asymptotic critical values*: 1% level 0.216000
5% level 0.146000
10% level 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
Residual variance (no correction) 7.217563
HAC corrected variance (Bartlett kernel) 77.26543
KPSS Test Equation
Dependent Variable: G10
Method: Least Squares
Date: 01/08/18 Time: 08:46
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 7.015508 0.356241 19.69315 0.0000
@TREND(1957Q1) -0.006112 0.002715 -2.251029 0.0253
R-squared 0.021929 Mean dependent var 6.321798
Adjusted R-squared 0.017602 S.D. dependent var 2.722480
S.E. of regression 2.698413 Akaike info criterion 4.831938
Sum squared resid 1645.604 Schwarz criterion 4.862020
Log likelihood -548.8410 Hannan-Quinn criter. 4.844075
F-statistic 5.067132 Durbin-Watson stat 0.031130
Prob(F-statistic) 0.025346
FINANCE WITH EVIEWS
Log likelihood -152.9773 Hannan-Quinn criter. 1.362716
Durbin-Watson stat 1.517887
The Computed t value is greater than the critical value. Therefore, the null hypothesis that the
series contain unit root is accepted implying G10 is not stationary at level.
Now, the result can be further supported by KPSS test.
Null Hypothesis: G10 is stationary
Exogenous: Constant, Linear Trend
Bandwidth: 11 (Newey-West automatic) using Bartlett kernel
LM-Stat.
Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.437056
Asymptotic critical values*: 1% level 0.216000
5% level 0.146000
10% level 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
Residual variance (no correction) 7.217563
HAC corrected variance (Bartlett kernel) 77.26543
KPSS Test Equation
Dependent Variable: G10
Method: Least Squares
Date: 01/08/18 Time: 08:46
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 7.015508 0.356241 19.69315 0.0000
@TREND(1957Q1) -0.006112 0.002715 -2.251029 0.0253
R-squared 0.021929 Mean dependent var 6.321798
Adjusted R-squared 0.017602 S.D. dependent var 2.722480
S.E. of regression 2.698413 Akaike info criterion 4.831938
Sum squared resid 1645.604 Schwarz criterion 4.862020
Log likelihood -548.8410 Hannan-Quinn criter. 4.844075
F-statistic 5.067132 Durbin-Watson stat 0.031130
Prob(F-statistic) 0.025346
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FINANCE WITH EVIEWS
The KPSS test rejects the null hypothesis that G10 is stationary at level. The calculated t value I
greater than the critical t value at all level of significance.
Therefore, the variable G10 is integrated of order 1.
Answer 4
genr SPREAD=g10-tb3ms
Order of integration for SPREAD
-2
-1
0
1
2
3
4
60 65 70 75 80 85 90 95 00 05 10
SPREAD
Graph of the variable ‘Spread’ shows a highly fluctuating trend with values fluctuating
mostly around zero.
Correlogram
FINANCE WITH EVIEWS
The KPSS test rejects the null hypothesis that G10 is stationary at level. The calculated t value I
greater than the critical t value at all level of significance.
Therefore, the variable G10 is integrated of order 1.
Answer 4
genr SPREAD=g10-tb3ms
Order of integration for SPREAD
-2
-1
0
1
2
3
4
60 65 70 75 80 85 90 95 00 05 10
SPREAD
Graph of the variable ‘Spread’ shows a highly fluctuating trend with values fluctuating
mostly around zero.
Correlogram
17
FINANCE WITH EVIEWS
ADF test
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.825366 0.0006
Test critical values: 1% level -3.999180
5% level -3.429834
10% level -3.138449
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:01
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
FINANCE WITH EVIEWS
ADF test
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.825366 0.0006
Test critical values: 1% level -3.999180
5% level -3.429834
10% level -3.138449
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:01
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
18
FINANCE WITH EVIEWS
SPREAD(-1) -0.158418 0.032830 -4.825366 0.0000
D(SPREAD(-1)) 0.246009 0.065049 3.781921 0.0002
C 0.125893 0.076101 1.654284 0.0995
@TREND(1957Q1) 0.001031 0.000584 1.763323 0.0792
R-squared 0.120122 Mean dependent var 0.009720
Adjusted R-squared 0.108232 S.D. dependent var 0.566687
S.E. of regression 0.535143 Akaike info criterion 1.604974
Sum squared resid 63.57584 Schwarz criterion 1.665514
Log likelihood -177.3621 Hannan-Quinn criter. 1.629406
F-statistic 10.10255 Durbin-Watson stat 1.961269
Prob(F-statistic) 0.000003
The ADF results shows the series does not contain unit root that is it is stationary at level.
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:05
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.158418 0.032830 -4.825366 0.0000
C 0.125893 0.076101 1.654284 0.0995
D(SPREAD(-1)) 0.246009 0.065049 3.781921 0.0002
@TREND 0.001031 0.000584 1.763323 0.0792
R-squared 0.120122 Mean dependent var 0.009720
Adjusted R-squared 0.108232 S.D. dependent var 0.566687
S.E. of regression 0.535143 Akaike info criterion 1.604974
Sum squared resid 63.57584 Schwarz criterion 1.665514
Log likelihood -177.3621 Hannan-Quinn criter. 1.629406
F-statistic 10.10255 Durbin-Watson stat 1.961269
Prob(F-statistic) 0.000003
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 4.794418 Prob. F(2,220) 0.0092
Obs*R-squared 9.438947 Prob. Chi-Square(2) 0.0089
The null hypothesis that the there is no first order auto correlation is rejected. This means the
residual are auto-correlated.
FINANCE WITH EVIEWS
SPREAD(-1) -0.158418 0.032830 -4.825366 0.0000
D(SPREAD(-1)) 0.246009 0.065049 3.781921 0.0002
C 0.125893 0.076101 1.654284 0.0995
@TREND(1957Q1) 0.001031 0.000584 1.763323 0.0792
R-squared 0.120122 Mean dependent var 0.009720
Adjusted R-squared 0.108232 S.D. dependent var 0.566687
S.E. of regression 0.535143 Akaike info criterion 1.604974
Sum squared resid 63.57584 Schwarz criterion 1.665514
Log likelihood -177.3621 Hannan-Quinn criter. 1.629406
F-statistic 10.10255 Durbin-Watson stat 1.961269
Prob(F-statistic) 0.000003
The ADF results shows the series does not contain unit root that is it is stationary at level.
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:05
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.158418 0.032830 -4.825366 0.0000
C 0.125893 0.076101 1.654284 0.0995
D(SPREAD(-1)) 0.246009 0.065049 3.781921 0.0002
@TREND 0.001031 0.000584 1.763323 0.0792
R-squared 0.120122 Mean dependent var 0.009720
Adjusted R-squared 0.108232 S.D. dependent var 0.566687
S.E. of regression 0.535143 Akaike info criterion 1.604974
Sum squared resid 63.57584 Schwarz criterion 1.665514
Log likelihood -177.3621 Hannan-Quinn criter. 1.629406
F-statistic 10.10255 Durbin-Watson stat 1.961269
Prob(F-statistic) 0.000003
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 4.794418 Prob. F(2,220) 0.0092
Obs*R-squared 9.438947 Prob. Chi-Square(2) 0.0089
The null hypothesis that the there is no first order auto correlation is rejected. This means the
residual are auto-correlated.
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FINANCE WITH EVIEWS
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 3.055670 Prob. F(3,222) 0.0293
Obs*R-squared 8.962110 Prob. Chi-Square(3) 0.0298
Scaled explained SS 39.45987 Prob. Chi-Square(3) 0.0000
The Breush- Pagan- Godfrey test reject the null hypothesis that disturbances are homoscedastic.
Therefore, heteroscadasticity is present in the series.
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.901564 0.0135
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 08:52
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
C 0.106656 0.077251 1.380633 0.1688
@TREND(1957Q1) 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
Dependent Variable: D(SPREAD)
Method: Least Squares
FINANCE WITH EVIEWS
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 3.055670 Prob. F(3,222) 0.0293
Obs*R-squared 8.962110 Prob. Chi-Square(3) 0.0298
Scaled explained SS 39.45987 Prob. Chi-Square(3) 0.0000
The Breush- Pagan- Godfrey test reject the null hypothesis that disturbances are homoscedastic.
Therefore, heteroscadasticity is present in the series.
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on Modified AIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.901564 0.0135
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 08:52
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
C 0.106656 0.077251 1.380633 0.1688
@TREND(1957Q1) 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
Dependent Variable: D(SPREAD)
Method: Least Squares
20
FINANCE WITH EVIEWS
Date: 01/08/18 Time: 08:54
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.106656 0.077251 1.380633 0.1688
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
@TREND 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 7.891104 Prob. F(2,222) 0.0005
Obs*R-squared 15.06657 Prob. Chi-Square(2) 0.0005
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 0.887991 Prob. F(2,224) 0.4129
Obs*R-squared 1.785610 Prob. Chi-Square(2) 0.4095
Scaled explained SS 6.593278 Prob. Chi-Square(2) 0.0370
The problem of Autocorrelation still remains. Therefore, Phillips-Perron test is used to examine
stationarity.
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -4.367145 0.0030
FINANCE WITH EVIEWS
Date: 01/08/18 Time: 08:54
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.106656 0.077251 1.380633 0.1688
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
@TREND 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 7.891104 Prob. F(2,222) 0.0005
Obs*R-squared 15.06657 Prob. Chi-Square(2) 0.0005
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 0.887991 Prob. F(2,224) 0.4129
Obs*R-squared 1.785610 Prob. Chi-Square(2) 0.4095
Scaled explained SS 6.593278 Prob. Chi-Square(2) 0.0370
The problem of Autocorrelation still remains. Therefore, Phillips-Perron test is used to examine
stationarity.
Null Hypothesis: SPREAD has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 3 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -4.367145 0.0030
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FINANCE WITH EVIEWS
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.298170
HAC corrected variance (Bartlett kernel) 0.383282
Phillips-Perron Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:13
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
C 0.106656 0.077251 1.380633 0.1688
@TREND(1957Q1) 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
The Phillips- Perron test gives the similar result as ADF test. The series does not contain any unit
root and hence is stationary at level.
Next, KPSS test is run to confirm stationarity of the variable.
Null Hypothesis: SPREAD is stationary
Exogenous: Constant, Linear Trend
Bandwidth: 10 (Newey-West automatic) using Bartlett kernel
LM-Stat.
Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.047063
Asymptotic critical values*: 1% level 0.216000
5% level 0.146000
10% level 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
FINANCE WITH EVIEWS
Test critical values: 1% level -3.998997
5% level -3.429745
10% level -3.138397
*MacKinnon (1996) one-sided p-values.
Residual variance (no correction) 0.298170
HAC corrected variance (Bartlett kernel) 0.383282
Phillips-Perron Test Equation
Dependent Variable: D(SPREAD)
Method: Least Squares
Date: 01/08/18 Time: 09:13
Sample (adjusted): 1957Q2 2013Q4
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
SPREAD(-1) -0.127266 0.032619 -3.901564 0.0001
C 0.106656 0.077251 1.380633 0.1688
@TREND(1957Q1) 0.000819 0.000595 1.376159 0.1701
R-squared 0.063632 Mean dependent var 0.010470
Adjusted R-squared 0.055272 S.D. dependent var 0.565545
S.E. of regression 0.549694 Akaike info criterion 1.654217
Sum squared resid 67.68456 Schwarz criterion 1.699481
Log likelihood -184.7536 Hannan-Quinn criter. 1.672481
F-statistic 7.611101 Durbin-Watson stat 1.570035
Prob(F-statistic) 0.000634
The Phillips- Perron test gives the similar result as ADF test. The series does not contain any unit
root and hence is stationary at level.
Next, KPSS test is run to confirm stationarity of the variable.
Null Hypothesis: SPREAD is stationary
Exogenous: Constant, Linear Trend
Bandwidth: 10 (Newey-West automatic) using Bartlett kernel
LM-Stat.
Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.047063
Asymptotic critical values*: 1% level 0.216000
5% level 0.146000
10% level 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
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22
FINANCE WITH EVIEWS
Residual variance (no correction) 1.246464
HAC corrected variance (Bartlett kernel) 6.800356
KPSS Test Equation
Dependent Variable: SPREAD
Method: Least Squares
Date: 01/08/18 Time: 09:15
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 0.758337 0.148043 5.122405 0.0000
@TREND(1957Q1) 0.006486 0.001128 5.748114 0.0000
R-squared 0.127551 Mean dependent var 1.494488
Adjusted R-squared 0.123690 S.D. dependent var 1.197910
S.E. of regression 1.121381 Akaike info criterion 3.075732
Sum squared resid 284.1938 Schwarz criterion 3.105814
Log likelihood -348.6334 Hannan-Quinn criter. 3.087869
F-statistic 33.04081 Durbin-Watson stat 0.254361
Prob(F-statistic) 0.000000
The computed t value is less than the critical value. Therefore, null hypothesis that SPREAD is
stationary is accepted.
As suggested from all the test results the variable SPREAD is stationary at level and therefore
has integration order of 0.
Co-integration test
Assuming both the variable G10 and TB3MS have same order of integration 1 and the
difference between these two returns are stationary at levels there may exists a long-term
relationship between these two variables.
FINANCE WITH EVIEWS
Residual variance (no correction) 1.246464
HAC corrected variance (Bartlett kernel) 6.800356
KPSS Test Equation
Dependent Variable: SPREAD
Method: Least Squares
Date: 01/08/18 Time: 09:15
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 0.758337 0.148043 5.122405 0.0000
@TREND(1957Q1) 0.006486 0.001128 5.748114 0.0000
R-squared 0.127551 Mean dependent var 1.494488
Adjusted R-squared 0.123690 S.D. dependent var 1.197910
S.E. of regression 1.121381 Akaike info criterion 3.075732
Sum squared resid 284.1938 Schwarz criterion 3.105814
Log likelihood -348.6334 Hannan-Quinn criter. 3.087869
F-statistic 33.04081 Durbin-Watson stat 0.254361
Prob(F-statistic) 0.000000
The computed t value is less than the critical value. Therefore, null hypothesis that SPREAD is
stationary is accepted.
As suggested from all the test results the variable SPREAD is stationary at level and therefore
has integration order of 0.
Co-integration test
Assuming both the variable G10 and TB3MS have same order of integration 1 and the
difference between these two returns are stationary at levels there may exists a long-term
relationship between these two variables.
23
FINANCE WITH EVIEWS
0
2
4
6
8
10
12
14
16
60 65 70 75 80 85 90 95 00 05 10
G10 TB3MS
Co-integrating regression
Dependent Variable: G10
Method: Least Squares
Date: 01/05/18 Time: 14:45
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 2.310526 0.136471 16.93054 0.0000
TB3MS 0.830954 0.024015 34.60127 0.0000
R-squared 0.841208 Mean dependent var 6.321798
Adjusted R-squared 0.840506 S.D. dependent var 2.722480
S.E. of regression 1.087270 Akaike info criterion 3.013950
Sum squared resid 267.1671 Schwarz criterion 3.044032
Log likelihood -341.5903 Hannan-Quinn criter. 3.026087
F-statistic 1197.248 Durbin-Watson stat 0.192142
Prob(F-statistic) 0.000000
Co-efficient of the variable TB3MS shows long term elasticity of G10 with respect to TB3MS.
The value of the estimated co-efficient is 0.830954. The variable TB3MS turns out to be
statistically significant. The R square value is 0.84. This means the model is a good fitted model.
FINANCE WITH EVIEWS
0
2
4
6
8
10
12
14
16
60 65 70 75 80 85 90 95 00 05 10
G10 TB3MS
Co-integrating regression
Dependent Variable: G10
Method: Least Squares
Date: 01/05/18 Time: 14:45
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 2.310526 0.136471 16.93054 0.0000
TB3MS 0.830954 0.024015 34.60127 0.0000
R-squared 0.841208 Mean dependent var 6.321798
Adjusted R-squared 0.840506 S.D. dependent var 2.722480
S.E. of regression 1.087270 Akaike info criterion 3.013950
Sum squared resid 267.1671 Schwarz criterion 3.044032
Log likelihood -341.5903 Hannan-Quinn criter. 3.026087
F-statistic 1197.248 Durbin-Watson stat 0.192142
Prob(F-statistic) 0.000000
Co-efficient of the variable TB3MS shows long term elasticity of G10 with respect to TB3MS.
The value of the estimated co-efficient is 0.830954. The variable TB3MS turns out to be
statistically significant. The R square value is 0.84. This means the model is a good fitted model.
24
FINANCE WITH EVIEWS
Reverse co-integrating regression
Dependent Variable: TB3MS
Method: Least Squares
Date: 01/05/18 Time: 14:46
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C -1.572502 0.201312 -7.811274 0.0000
G10 1.012340 0.029257 34.60127 0.0000
R-squared 0.841208 Mean dependent var 4.827310
Adjusted R-squared 0.840506 S.D. dependent var 3.004965
S.E. of regression 1.200085 Akaike info criterion 3.211395
Sum squared resid 325.4862 Schwarz criterion 3.241477
Log likelihood -364.0991 Hannan-Quinn criter. 3.223533
F-statistic 1197.248 Durbin-Watson stat 0.222165
Prob(F-statistic) 0.000000
The long-term elasticity of TB3MS with respect to G10 is 1.012340. Same as forward co-
integration regression, the reverse regression also has a high value of R square and produce
statistically significant results.
Engel Granger test
Date: 01/05/18 Time: 13:53
Series: G10 TB3MS
Sample: 1957Q1 2013Q4
Included observations: 228
Null hypothesis: Series are not cointegrated
Cointegrating equation deterministics: C
Automatic lags specification based on Schwarz criterion (maxlag=14)
Dependent tau-statistic Prob.* z-statistic Prob.*
G10 -4.185075 0.0047 -34.47855 0.0018
TB3MS -4.487030 0.0017 -40.74978 0.0004
*MacKinnon (1996) p-values.
Intermediate Results:
G10 TB3MS
Rho – 1 -0.119745 -0.137916
Rho S.E. 0.028612 0.030737
Residual variance 0.207124 0.287865
Long-run residual variance 0.336199 0.492029
FINANCE WITH EVIEWS
Reverse co-integrating regression
Dependent Variable: TB3MS
Method: Least Squares
Date: 01/05/18 Time: 14:46
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C -1.572502 0.201312 -7.811274 0.0000
G10 1.012340 0.029257 34.60127 0.0000
R-squared 0.841208 Mean dependent var 4.827310
Adjusted R-squared 0.840506 S.D. dependent var 3.004965
S.E. of regression 1.200085 Akaike info criterion 3.211395
Sum squared resid 325.4862 Schwarz criterion 3.241477
Log likelihood -364.0991 Hannan-Quinn criter. 3.223533
F-statistic 1197.248 Durbin-Watson stat 0.222165
Prob(F-statistic) 0.000000
The long-term elasticity of TB3MS with respect to G10 is 1.012340. Same as forward co-
integration regression, the reverse regression also has a high value of R square and produce
statistically significant results.
Engel Granger test
Date: 01/05/18 Time: 13:53
Series: G10 TB3MS
Sample: 1957Q1 2013Q4
Included observations: 228
Null hypothesis: Series are not cointegrated
Cointegrating equation deterministics: C
Automatic lags specification based on Schwarz criterion (maxlag=14)
Dependent tau-statistic Prob.* z-statistic Prob.*
G10 -4.185075 0.0047 -34.47855 0.0018
TB3MS -4.487030 0.0017 -40.74978 0.0004
*MacKinnon (1996) p-values.
Intermediate Results:
G10 TB3MS
Rho – 1 -0.119745 -0.137916
Rho S.E. 0.028612 0.030737
Residual variance 0.207124 0.287865
Long-run residual variance 0.336199 0.492029
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25
FINANCE WITH EVIEWS
Number of lags 1 1
Number of observations 226 226
Number of stochastic trends** 2 2
**Number of stochastic trends in asymptotic distribution
The t statistics for the variable G10 and TB3MS are -4.185075 and -4.487030. P values
for both the statistics are 0.0000. The null hypothesis for Engel Granger test for co-integration
states that there is no co-integration between the variables. The null hypothesis is rejected here
and therefore, a stable long-term relation exists between the variables.
Dependent Variable: G10
Method: Least Squares
Date: 01/08/18 Time: 09:21
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 2.310526 0.136471 16.93054 0.0000
TB3MS 0.830954 0.024015 34.60127 0.0000
R-squared 0.841208 Mean dependent var 6.321798
Adjusted R-squared 0.840506 S.D. dependent var 2.722480
S.E. of regression 1.087270 Akaike info criterion 3.013950
Sum squared resid 267.1671 Schwarz criterion 3.044032
Log likelihood -341.5903 Hannan-Quinn criter. 3.026087
F-statistic 1197.248 Durbin-Watson stat 0.192142
Prob(F-statistic) 0.000000
Null Hypothesis: E has a unit root
Exogenous: None
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.185075 0.0000
Test critical values: 1% level -2.575234
5% level -1.942236
10% level -1.615764
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(E)
Method: Least Squares
FINANCE WITH EVIEWS
Number of lags 1 1
Number of observations 226 226
Number of stochastic trends** 2 2
**Number of stochastic trends in asymptotic distribution
The t statistics for the variable G10 and TB3MS are -4.185075 and -4.487030. P values
for both the statistics are 0.0000. The null hypothesis for Engel Granger test for co-integration
states that there is no co-integration between the variables. The null hypothesis is rejected here
and therefore, a stable long-term relation exists between the variables.
Dependent Variable: G10
Method: Least Squares
Date: 01/08/18 Time: 09:21
Sample: 1957Q1 2013Q4
Included observations: 228
Variable Coefficient Std. Error t-Statistic Prob.
C 2.310526 0.136471 16.93054 0.0000
TB3MS 0.830954 0.024015 34.60127 0.0000
R-squared 0.841208 Mean dependent var 6.321798
Adjusted R-squared 0.840506 S.D. dependent var 2.722480
S.E. of regression 1.087270 Akaike info criterion 3.013950
Sum squared resid 267.1671 Schwarz criterion 3.044032
Log likelihood -341.5903 Hannan-Quinn criter. 3.026087
F-statistic 1197.248 Durbin-Watson stat 0.192142
Prob(F-statistic) 0.000000
Null Hypothesis: E has a unit root
Exogenous: None
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.185075 0.0000
Test critical values: 1% level -2.575234
5% level -1.942236
10% level -1.615764
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(E)
Method: Least Squares
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FINANCE WITH EVIEWS
Date: 01/08/18 Time: 09:22
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) -0.119745 0.028612 -4.185075 0.0000
D(E(-1)) 0.215095 0.064988 3.309754 0.0011
R-squared 0.095359 Mean dependent var 0.007418
Adjusted R-squared 0.091320 S.D. dependent var 0.477430
S.E. of regression 0.455109 Akaike info criterion 1.272251
Sum squared resid 46.39584 Schwarz criterion 1.302521
Log likelihood -141.7644 Hannan-Quinn criter. 1.284467
Durbin-Watson stat 1.971453
The residual is stationary at level. The residuals are assumed to be non-auto correlated. The
assumption can be verified by conducting relevant autocorrelation test.
Dependent Variable: D(E)
Method: Least Squares
Date: 01/08/18 Time: 09:25
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) -0.119745 0.028612 -4.185075 0.0000
D(E(-1)) 0.215095 0.064988 3.309754 0.0011
R-squared 0.095359 Mean dependent var 0.007418
Adjusted R-squared 0.091320 S.D. dependent var 0.477430
S.E. of regression 0.455109 Akaike info criterion 1.272251
Sum squared resid 46.39584 Schwarz criterion 1.302521
Log likelihood -141.7644 Hannan-Quinn criter. 1.284467
Durbin-Watson stat 1.971453
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 2.346576 Prob. F(2,222) 0.0981
Obs*R-squared 4.636859 Prob. Chi-Square(2) 0.0984
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 01/08/18 Time: 09:26
Sample: 1957Q3 2013Q4
Included observations: 226
FINANCE WITH EVIEWS
Date: 01/08/18 Time: 09:22
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) -0.119745 0.028612 -4.185075 0.0000
D(E(-1)) 0.215095 0.064988 3.309754 0.0011
R-squared 0.095359 Mean dependent var 0.007418
Adjusted R-squared 0.091320 S.D. dependent var 0.477430
S.E. of regression 0.455109 Akaike info criterion 1.272251
Sum squared resid 46.39584 Schwarz criterion 1.302521
Log likelihood -141.7644 Hannan-Quinn criter. 1.284467
Durbin-Watson stat 1.971453
The residual is stationary at level. The residuals are assumed to be non-auto correlated. The
assumption can be verified by conducting relevant autocorrelation test.
Dependent Variable: D(E)
Method: Least Squares
Date: 01/08/18 Time: 09:25
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) -0.119745 0.028612 -4.185075 0.0000
D(E(-1)) 0.215095 0.064988 3.309754 0.0011
R-squared 0.095359 Mean dependent var 0.007418
Adjusted R-squared 0.091320 S.D. dependent var 0.477430
S.E. of regression 0.455109 Akaike info criterion 1.272251
Sum squared resid 46.39584 Schwarz criterion 1.302521
Log likelihood -141.7644 Hannan-Quinn criter. 1.284467
Durbin-Watson stat 1.971453
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 2.346576 Prob. F(2,222) 0.0981
Obs*R-squared 4.636859 Prob. Chi-Square(2) 0.0984
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 01/08/18 Time: 09:26
Sample: 1957Q3 2013Q4
Included observations: 226
27
FINANCE WITH EVIEWS
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) 0.311936 0.181632 1.717405 0.0873
D(E(-1)) 1.773346 1.090550 1.626102 0.1053
RESID(-1) -2.062660 1.266708 -1.628363 0.1049
RESID(-2) -0.595627 0.308975 -1.927749 0.0552
R-squared 0.020517 Mean dependent var 0.006237
Adjusted R-squared 0.007281 S.D. dependent var 0.454054
S.E. of regression 0.452398 Akaike info criterion 1.269030
Sum squared resid 45.43533 Schwarz criterion 1.329571
Log likelihood -139.4004 Hannan-Quinn criter. 1.293462
Durbin-Watson stat 1.991709
As shown above, the LM test result fail to reject the null hypothesis that there are no
serial autocorrelation.
Answer 5
Error Correction Model
Any stable relation in the long-run passes with some short-term adjustment. The
fluctuations or error in the short-run is corrected and this is modeled with error correction model.
Two-vector error correction model is framed here. Error correction mode is constructed for both
co-integrating regression and reverse co-integration regression.
∆ TB 3 MSt=α1 +α 2 TB 3 MSt−1 +α3 TB 3 MSt −2+ α 4 G 10t −1+ α5 G10t−2 +α6 SPREADt−1 +ε t
∆ G 10t =β1+β2 TB3 MSt −1 + β3 TB3 MSt−2 + β4 G10t−1 +β5 G 10t −2 +β6 SPREADt −1+εt
Dependent Variable: DTB3MS
Method: Least Squares
Date: 01/05/18 Time: 15:33
Sample (adjusted): 1957Q4 2013Q4
Included observations: 225 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.074671 0.080399 -0.928751 0.3540
DTB3MS(-1) 0.249607 0.085885 2.906308 0.0040
FINANCE WITH EVIEWS
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) 0.311936 0.181632 1.717405 0.0873
D(E(-1)) 1.773346 1.090550 1.626102 0.1053
RESID(-1) -2.062660 1.266708 -1.628363 0.1049
RESID(-2) -0.595627 0.308975 -1.927749 0.0552
R-squared 0.020517 Mean dependent var 0.006237
Adjusted R-squared 0.007281 S.D. dependent var 0.454054
S.E. of regression 0.452398 Akaike info criterion 1.269030
Sum squared resid 45.43533 Schwarz criterion 1.329571
Log likelihood -139.4004 Hannan-Quinn criter. 1.293462
Durbin-Watson stat 1.991709
As shown above, the LM test result fail to reject the null hypothesis that there are no
serial autocorrelation.
Answer 5
Error Correction Model
Any stable relation in the long-run passes with some short-term adjustment. The
fluctuations or error in the short-run is corrected and this is modeled with error correction model.
Two-vector error correction model is framed here. Error correction mode is constructed for both
co-integrating regression and reverse co-integration regression.
∆ TB 3 MSt=α1 +α 2 TB 3 MSt−1 +α3 TB 3 MSt −2+ α 4 G 10t −1+ α5 G10t−2 +α6 SPREADt−1 +ε t
∆ G 10t =β1+β2 TB3 MSt −1 + β3 TB3 MSt−2 + β4 G10t−1 +β5 G 10t −2 +β6 SPREADt −1+εt
Dependent Variable: DTB3MS
Method: Least Squares
Date: 01/05/18 Time: 15:33
Sample (adjusted): 1957Q4 2013Q4
Included observations: 225 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.074671 0.080399 -0.928751 0.3540
DTB3MS(-1) 0.249607 0.085885 2.906308 0.0040
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28
FINANCE WITH EVIEWS
DTB3MS(-2) -0.167745 0.088189 -1.902110 0.0585
DG10(-1) 0.137923 0.131189 1.051325 0.2943
DG10(-2) -0.145302 0.132433 -1.097173 0.2738
SPREAD(-1) 0.040613 0.043878 0.925579 0.3557
R-squared 0.121683 Mean dependent var -0.014622
Adjusted R-squared 0.101631 S.D. dependent var 0.743589
S.E. of regression 0.704791 Akaike info criterion 2.164474
Sum squared resid 108.7840 Schwarz criterion 2.255570
Log likelihood -237.5033 Hannan-Quinn criter. 2.201241
F-statistic 6.068123 Durbin-Watson stat 1.861422
Prob(F-statistic) 0.000028
The error correction model as estimated above shows changes in TB3MS due to changes
in explanatory variables. Not all variables are statistically significant. Only DB3MSt-1.
Therefore, in the next step, all the insignificant variables are eliminated and the
consequent estimated equation is given below
Dependent Variable: DTB3MS
Method: Least Squares
Date: 01/06/18 Time: 08:13
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.010486 0.048146 -0.217795 0.8278
DTB3MS(-1) 0.230740 0.065012 3.549196 0.0005
R-squared 0.053242 Mean dependent var -0.013614
Adjusted R-squared 0.049015 S.D. dependent var 0.742090
S.E. of regression 0.723674 Akaike info criterion 2.199859
Sum squared resid 117.3098 Schwarz criterion 2.230130
Log likelihood -246.5841 Hannan-Quinn criter. 2.212075
F-statistic 12.59679 Durbin-Watson stat 1.886197
Prob(F-statistic) 0.000471
Dependent Variable: DG10
FINANCE WITH EVIEWS
DTB3MS(-2) -0.167745 0.088189 -1.902110 0.0585
DG10(-1) 0.137923 0.131189 1.051325 0.2943
DG10(-2) -0.145302 0.132433 -1.097173 0.2738
SPREAD(-1) 0.040613 0.043878 0.925579 0.3557
R-squared 0.121683 Mean dependent var -0.014622
Adjusted R-squared 0.101631 S.D. dependent var 0.743589
S.E. of regression 0.704791 Akaike info criterion 2.164474
Sum squared resid 108.7840 Schwarz criterion 2.255570
Log likelihood -237.5033 Hannan-Quinn criter. 2.201241
F-statistic 6.068123 Durbin-Watson stat 1.861422
Prob(F-statistic) 0.000028
The error correction model as estimated above shows changes in TB3MS due to changes
in explanatory variables. Not all variables are statistically significant. Only DB3MSt-1.
Therefore, in the next step, all the insignificant variables are eliminated and the
consequent estimated equation is given below
Dependent Variable: DTB3MS
Method: Least Squares
Date: 01/06/18 Time: 08:13
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.010486 0.048146 -0.217795 0.8278
DTB3MS(-1) 0.230740 0.065012 3.549196 0.0005
R-squared 0.053242 Mean dependent var -0.013614
Adjusted R-squared 0.049015 S.D. dependent var 0.742090
S.E. of regression 0.723674 Akaike info criterion 2.199859
Sum squared resid 117.3098 Schwarz criterion 2.230130
Log likelihood -246.5841 Hannan-Quinn criter. 2.212075
F-statistic 12.59679 Durbin-Watson stat 1.886197
Prob(F-statistic) 0.000471
Dependent Variable: DG10
29
FINANCE WITH EVIEWS
Method: Least Squares
Date: 01/05/18 Time: 15:36
Sample (adjusted): 1957Q4 2013Q4
Included observations: 225 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.116314 0.052193 2.228559 0.0269
DTB3MS(-1) -2.08E-05 0.055754 -0.000373 0.9997
DTB3MS(-2) -0.070522 0.057250 -1.231828 0.2193
DG10(-1) 0.235052 0.085164 2.759992 0.0063
DG10(-2) -0.072607 0.085971 -0.844547 0.3993
SPREAD(-1) -0.081396 0.028484 -2.857579 0.0047
R-squared 0.102533 Mean dependent var -0.005244
Adjusted R-squared 0.082043 S.D. dependent var 0.477537
S.E. of regression 0.457528 Akaike info criterion 1.300349
Sum squared resid 45.84378 Schwarz criterion 1.391445
Log likelihood -140.2893 Hannan-Quinn criter. 1.337116
F-statistic 5.004005 Durbin-Watson stat 1.946316
Prob(F-statistic) 0.000232
The error correction model as estimated above shows changes in G10 due to changes in
explanatory variables. Not all variables are statistically significant. Only two variables are
statistically significant. These two variables are G10t-1 and SPREADt-1.
The insignificant variables are eliminated and regression is run considering only
significant variables.
Dependent Variable: DG10
Method: Least Squares
Date: 01/06/18 Time: 08:17
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.087644 0.049511 1.770198 0.0781
DG10(-1) 0.209355 0.065502 3.196146 0.0016
SPREAD(-1) -0.060821 0.026088 -2.331330 0.0206
R-squared 0.079901 Mean dependent var -0.003894
Adjusted R-squared 0.071649 S.D. dependent var 0.476907
S.E. of regression 0.459504 Akaike info criterion 1.295849
Sum squared resid 47.08518 Schwarz criterion 1.341254
Log likelihood -143.4309 Hannan-Quinn criter. 1.314173
F-statistic 9.682625 Durbin-Watson stat 1.944802
FINANCE WITH EVIEWS
Method: Least Squares
Date: 01/05/18 Time: 15:36
Sample (adjusted): 1957Q4 2013Q4
Included observations: 225 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.116314 0.052193 2.228559 0.0269
DTB3MS(-1) -2.08E-05 0.055754 -0.000373 0.9997
DTB3MS(-2) -0.070522 0.057250 -1.231828 0.2193
DG10(-1) 0.235052 0.085164 2.759992 0.0063
DG10(-2) -0.072607 0.085971 -0.844547 0.3993
SPREAD(-1) -0.081396 0.028484 -2.857579 0.0047
R-squared 0.102533 Mean dependent var -0.005244
Adjusted R-squared 0.082043 S.D. dependent var 0.477537
S.E. of regression 0.457528 Akaike info criterion 1.300349
Sum squared resid 45.84378 Schwarz criterion 1.391445
Log likelihood -140.2893 Hannan-Quinn criter. 1.337116
F-statistic 5.004005 Durbin-Watson stat 1.946316
Prob(F-statistic) 0.000232
The error correction model as estimated above shows changes in G10 due to changes in
explanatory variables. Not all variables are statistically significant. Only two variables are
statistically significant. These two variables are G10t-1 and SPREADt-1.
The insignificant variables are eliminated and regression is run considering only
significant variables.
Dependent Variable: DG10
Method: Least Squares
Date: 01/06/18 Time: 08:17
Sample (adjusted): 1957Q3 2013Q4
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.087644 0.049511 1.770198 0.0781
DG10(-1) 0.209355 0.065502 3.196146 0.0016
SPREAD(-1) -0.060821 0.026088 -2.331330 0.0206
R-squared 0.079901 Mean dependent var -0.003894
Adjusted R-squared 0.071649 S.D. dependent var 0.476907
S.E. of regression 0.459504 Akaike info criterion 1.295849
Sum squared resid 47.08518 Schwarz criterion 1.341254
Log likelihood -143.4309 Hannan-Quinn criter. 1.314173
F-statistic 9.682625 Durbin-Watson stat 1.944802
30
FINANCE WITH EVIEWS
Prob(F-statistic) 0.000093
The speed of adjustment is -0.060821.
FINANCE WITH EVIEWS
Prob(F-statistic) 0.000093
The speed of adjustment is -0.060821.
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