Time series analysis use E-views programer

1
Workshop on:
Using the E-views.9 program
Introduction
STEP 1: UnitRoot Tests
STEP 2: Estimatethe MultivariateVECM Model
STEP 2.1:Select the Optimum Lag Length
STEP 2.2:Johansen Co-integration Test
STEP 2.3:VECM Model
STEP 2.4:Grangercausalitytest
STEP 2.5:Variancedecomposition (VDC)
STEP 2.6:Impulseresponse functions(IRFs)
Prof.Dr.Nabeel Aljanabi
University of Al-Qadisiyah -Iraq

2
Introduction
This workshop explains the steps to carry out Unit Root tests, Johansen co-integration test,
Granger Causality, variance decomposition and Impulse response functions.
This example analyzes the importance of the monetary policy and its transmission mechanism in
the fast-growing Bahrain economy. The monetary model is:
M3 = f(Y, R, P) (1)
where M3 is money supply; Y is oil production index, R is Interest Rate, and P is Consumer
Price Index (CPI).
The data file is covering from 1980M1 to 2008:M12.

3
Year M3 R P Y
1980M1 26281.8 3.49 46.1 12.54
1980M2 27301 3.59 46.21 12.61
1980M3 27926 3.66 46.28 13.22
1980M4 28721.9 3.75 46.13 13.56
1980M5 29483 4.1 46.49 13.72
1980M6 30130 4.17 46.86 12.93
1980M7 30747.6 4.14 47.36 14.06
1980M8 31157.6 4.14 47.78 13.29
1980M9 30864 4.26 47.62 13.95
1980M10 31272.7 4.33 47.89 13.83
1980M11 31906.4 4.47 48.54 13.56
1980M12 32687.6 4.46 48.94 13.39
1981M1 34458.1 4.42 49.78 13.06
: : : : :
: : : : :
: : : : :
2008M9 912780 3.56 114.73 105.04
2008M10 900443 3.55 114.23 104.35
2008M11 909231 3.38 112.93 100.38
2008M12 931656 3.02 111.83 95.92
1. Open E-view 9 – File – New -- Work file

4
2. Choose the frequency as Monthly – from 1980 M1 to 2008 M12 and then Click “OK”
3. Click the button “Quick” and “Empty Group (Edit Series)”
Place your cursor to the left of the first row (obs)

5
4. Copy the original data from Excel file.
5. Paste the data to E-view worksheet

6
6. Transform the variables into logarithm from [Type the following generate (genr)
command]:
genr lm3 = log(m3)
genr lp = log(p)
genr lr = log(r)
genr ly = log(y)
STEP 1: UnitRoot Tests

7
7. Checking for Unit Root – For example: lm3. Double click on “lm3”, click “View” and
choose the Unit Root Test.
8. We can choose Augmented Dickey Fuller (ADF) test and the optimal lag length is
selected by Akaike Information Criteria (large sample size).
i) First, we perform the unit root test of “lm3”: level model with constant but
without trend model (let say the maximum lag is 16) .
ii) Second, we perform the Unit root test again for the level model but now with
constant with trend model.

8
E-view Output for level Unit Root Test:
Constant without Trend Model:
Null Hypothesis:LM3 has a unit root
Exogenous: Constant
Lag Length: 16 (Automatic based on AIC, MAXLAG=16)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.166712 0.6897
Test critical values: 1% level -3.449917
5% level -2.870057
10% level -2.571377
*MacKinnon (1996) one-sided p-values.
Constant with Trend Model:
Exogenous: Constant, Linear Trend
t-Statistic Prob.*
5% level -3.423418
10% level -3.134664
After that, we estimate the first difference with and without trend models (repeat the
same process but now select 1st difference).

9
E-view Output for First Different Unit Root Test:
Constant without Trend Model:
Null Hypothesis:D(LM3) has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.870031
10% level -2.571363
Constant with Trend Model:
Exogenous: Constant, Linear Trend
t-Statistic Prob.*
5% level -3.423459
10% level -3.134688
9. We also can perform another unit root test namely Phillips-Perron (PP) test.
E-views Output:

10
i. Level, Constant Without Trend
Exogenous:Constant
Bandwidth:9 (Newey-Westusing Bartlett kernel)
Adj. t-Stat Prob.*
Phillips-Perron teststatistic -2.469495 0.1239
5% level -2.869653
10% level -2.571161
ii. Level, Constant With Trend
Exogenous:Constant,Linear Trend
Adj. t-Stat Prob.*
5% level -3.422828
10% level -3.134315
iii. First Difference, Constant Without Trend
Exogenous:Constant
Adj. t-Stat Prob.*
5% level -2.869677
10% level -2.571174
iv. First Difference, Constant With Trend

11
Exogenous:Constant,Linear Trend
Adj. t-Stat Prob.*
5% level -3.422865
10% level -3.134337
Table 1 below presents the results of Unit Root Tests:
Table 1 Unit Root Tests
Augmented Dickey Fuller
(ADF)
Phillips Perron
(PP)
Level
Variable Constant
Without Trend
Constant
With Trend
Constant
Without Trend
Constant
With Trend
LM3 -1.1667
(16)
-1.5593
(15)
-2.4695
[9]
-1.0419
[9]
LP
LR
LY
First Difference
LM3 -2.866**
(14)
-3.0513
(15)
-16.6246***
[9]
-16.7362***
[8]
LP
LR
LY
Note: *** and ** denotes significant at 1%, and 5% significance level, respectively. The figure in
parenthesis (…) represents optimum lag length selected based on Akaike Info Critirion. The figure in
bracket […] represents the Bandwidth used in the KPSS test selected based on Newey-West
Bandwidth critirion.
Please complete the above results of Unit Root Tests
STEP 2: Estimatethe MultivariateVECM Model

12
10. After testing the variables are stationary at first order or I(1), then the step is to estimate
the Vector Error-correction Model (VECM). Firstly, we need to select an optimum lag of
VECM model before performing the Johansen cointegration test.
(You should show all the four log variables).
Then click “Quick” – “Estimate VAR” – “Vector Error Correction”

13
11. From equation (1), the VECM model can be written as:
∆𝐿𝑀31𝑡 = 𝜇1𝑡 − ∅1(𝐿𝑀3− 𝛾0 − 𝛾1 𝐿𝑌 − 𝛾2 𝐿𝑅 − 𝛾3 𝐿𝑃) 𝑡−1 + ∑ 𝛽1,𝑗 ∆𝐿𝑀31𝑡−𝑖
𝑗
𝑖=1 +
∑ 𝛽2,𝑗 ∆𝐿𝑌1𝑡−𝑖 + ∑ 𝛽3,𝑗 ∆𝐿𝑅1𝑡−𝑖 + ∑ ∆𝐿𝑃1𝑡−𝑖 + 𝜀1𝑡
𝑗
𝑖=1
𝑗
𝑖=1
𝑗
𝑖=1
(2)
∆𝐿𝑌2𝑡 = 𝜇2𝑡 − ∅2 (𝐿𝑀3 − 𝛾0 − 𝛾1 𝐿𝑌 − 𝛾2 𝐿𝑅 − 𝛾3 𝐿𝑃) 𝑡−1 + ∑ ∆𝐿𝑀32𝑡−𝑖
𝑗
𝑖=1 +
∑ ∆𝐿𝑌2𝑡−𝑖 + ∑ ∆𝐿𝑅2𝑡−𝑖 + ∑ ∆𝐿𝑃2𝑡−𝑖 + 𝜀2𝑡
𝑗
𝑖=1
𝑗
𝑖=1
𝑗
𝑖=1
(3)
∆𝐿𝑅3𝑡 = 𝜇3𝑡 − ∅3(𝐿𝑀3 − 𝛾0 − 𝛾1 𝐿𝑌 − 𝛾2 𝐿𝑅 − 𝛾3 𝐿𝑃) 𝑡−1 + ∑ ∆𝐿𝑀33𝑡−𝑖
𝑗
𝑖=1 +
∑ ∆𝐿𝑌3𝑡−𝑖 + ∑ ∆𝐿𝑅3𝑡−𝑖 + ∑ ∆𝐿𝑃3𝑡−𝑖 + 𝜀3𝑡
𝑗
𝑖=1
𝑗
𝑖=1
𝑗
𝑖=1
(4)
∆𝐿𝑃4𝑡 = 𝜇4𝑡 − ∅4(𝐿𝑀3− 𝛾0 − 𝛾1 𝐿𝑌 − 𝛾2 𝐿𝑅 − 𝛾3 𝐿𝑃) 𝑡−1 + ∑ ∆𝐿𝑀34𝑡−𝑖
𝑗
𝑖=1 +
∑ ∆𝐿𝑌4𝑡−𝑖 + ∑ ∆𝐿𝑅4𝑡−𝑖 + ∑ ∆𝐿𝑃4𝑡−𝑖 + 𝜀4𝑡
𝑗
𝑖=1
𝑗
𝑖=1
𝑗
𝑖=1
(5)

14
STEP 2.1: Select the Optimum Lag Length
(a) First, we estimate the VECM model with lag 1
(b) Make residuals for the VECM models, click “Proc” – “Make Residuals”
EViews will show 4 residuals in the EViews Workfile – resid01 (residual in Equation 1),
resid02 (residual in Equation 2), resid03 (residual in Equation 3), and resid04 (residual in
Equation 4).
Type in all variables with
lm3 first (dependent
variable)
LM3 LY LR LP
Change 2 to 1

15
(c) Now, the autocorrelation of the error terms in each regression is checked by using the
Ljung-Box Q-statistic.
We double click the “resid01” – “View” – “Correlogram…” – “OK”

16
E-Views Output:
The Q-statistic shows that the error terms are statistically significant from lag 12 for
“resid01”. This indicates that the model with lag 1 has autocorrelation problem. Hence,
we need to re-estimate the VECM model by increasing one lag (repeat the same process
but now with lag 2).
This process will continue until each of the regression error terms is free from
autocorrelation problem (where the p-values of Q-statistic are greater than 0.05).
In this case, we repeat the same process and the optimum lag is 12.
The p-value is less
than 0.05. This
implies that the
regression residuals
have autocorrelation
problem.

17
12. The E-Views output with 12 lag is as follows:
STEP 2.2:Johansen Co-integration Test
13. After obtaining the optimum lag, the next step is to estimate the Johansen Co-integration
Test. Click “View” – “Co-integration Test” – “OK”.
Error
correction
terms
(ECT)
Long-run
Equation

18
E-Views Output:
Sample (adjusted):1981M02 2008M12
Included observations:335 after adjustments
Trend assumption:Linear deterministic trend
Series:LM3 LP LR LY
Lags interval (in first differences):1 to 12
Unrestricted Cointegration Rank Test(Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.088734 51.98841 47.85613 0.0194
At most 1 0.043366 20.86000 29.79707 0.3664
At most 2 0.014884 6.007864 15.49471 0.6946
At most 3 0.002934 0.984286 3.841466 0.3211
Trace test indicates 1 cointegrating eqn(s) atthe 0.05 level
* denotes rejection ofthe 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 * 0.088734 31.12841 27.58434 0.0168
At most 1 0.043366 14.85214 21.13162 0.2994
At most 2 0.014884 5.023578 14.26460 0.7388
At most 3 0.002934 0.984286 3.841466 0.3211
0.05 represent 5%
significance level.

19
Max-eigenvalue test indicates 1 co-integrating eqn(s) atthe 0.05 level
* denotes rejection ofthe hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Table 2 presents the Johansen-Juselius Co-integration test. The result shows that both
Trace test and Max-Eigen test are statistically significant to reject the null hypothesis of r
= 0 at 5% significance level. Therefore, only one long run co-integration relationship
between M3 and it determinants.
Table 2: Johansen-Juselius Co-integration Tests
Hypothesized Trace Max-Eigen Critical Values (5%)
No. of CE(s) Statistic Statistic Trace Max-Eigen
r = 0 51.9884** 31.1284** 47.856 27.584
r ≤ 1 20.860 14.852 29.797 21.132
r ≤ 2 6.0078 5.0235 15.495 14.265
r ≤ 3 0.9843 0.9843 3.8415 3.8415
Note: ** denotes significant at 5% significance levels.
STEP 2.3:VECM Model
If the model contains co-integration relationship among the variables, then we can
proceed to VECM and the long run equation is:
LM3t-1 = - 5.0146 + 3.6031 LPt-1 + 0.2233 LRt-1+ 0.3357 LYt-1
s.e (0.2872) (0.0494) (0.0946)
t-stat [12.5459] [4.5212] [3.5477]
All variables are positively significant at 5% significance level.
You can write this
equation by referring to
page 15 (but the
coefficient signs are now
reversed, why?)

20
STEP 2.4: Grangercausalitytest
14. After estimating the long-run VECM model, then we proceed to the short run Granger
causality test. Click “View” – “Lag Structure” – “Granger Causality/Block Exogeneity
Tests”.
E-Views Output:
VEC Granger Causality/Block Exogeneity Wald Tests
Sample:1980M01 2008M12
Included observations:335
Dependentvariable:D(LM3)
Excluded Chi-sq df Prob.
D(LP) 30.22932 12 0.0026
D(LR) 14.72288 12 0.2569
D(LY) 21.50639 12 0.0434
All 67.21100 36 0.0012

21
Dependentvariable:D(LP)
D(LM3) 23.98443 12 0.0204
D(LR) 23.39792 12 0.0245
D(LY) 23.92561 12 0.0208
All 63.26058 36 0.0033
Dependentvariable:D(LR)
D(LM3) 15.82326 12 0.1995
D(LP) 12.32216 12 0.4202
D(LY) 13.98317 12 0.3018
All 36.82666 36 0.4305
Dependentvariable:D(LY)
D(LM3) 17.93616 12 0.1176
D(LP) 16.41443 12 0.1730
D(LR) 10.79759 12 0.5463
All 48.57377 36 0.0786
With Co-integration, the dynamic causal interactions among the variables should be
phrased in a vector error correction form. This allows us to assess both long-run and
short-run causality, respectively, on the 2
 -test of the lagged first differenced terms for
each right-hand-side variable and the t-test of the error correction term. The results of the
test are presented in Table 3.

22
Table 3: Granger Causality Results based on VECM
Independent Variables
Dependent 2
 -statistics of lagged 1st
differenced term
[p-value]
ECTt-1
coefficient
Variable ΔLM3 ΔLP ΔLR ΔLY (t-ratio)
ΔLM3
--
30.23***
[0.003]
14.72
[0.257]
21.51**
[0.043]
-0.028**
(-3.533)
ΔLP 23.98**
[0.020] --
23.39**
[0.024]
23.93**
[0.021]
0.009**
(2.800)
ΔLR 15.82
[0.199]
12.32
[0.420] --
13.98
[0.302]
0.124
(1.947)
ΔLY 17.93
[0.118]
16.41
[0.173]
10.79
[0.546] --
0.093
(2.052)
Note: *** and ** denotessignificant at 1% and 5% significance level, respectively.The figure in the
parenthesis(…) denote as t-statistic and the figure in the squared brackets […] represent as p-value.
and the causal channels can be summarized as below:
LM3 LP
LY LR

23
STEP 2.5: Variancedecomposition (VDC)
15. The result of VECM indicates the erogeneity or endogeneity of a variable in the system
and the direction of Granger-causality within the sample period. However, it does not
provide us with the dynamic properties of the system. The analysis of the dynamic
interactions among the variables in the post-sample period is conducted through variance
decompositions (VDCs) and impulse response functions (IRFs).
E-Views Output:
Variance Decomposition of
LM3:
Period S.E. LM3 LP LR LY
1 0.009207 100.0000 0.000000 0.000000 0.000000
2 0.012581 99.59571 0.237534 7.15E-06 0.166753
3 0.015458 99.50123 0.242707 0.022763 0.233302
4 0.018050 98.21271 0.478537 0.134646 1.174103
5 0.020777 94.57704 1.376087 1.117796 2.929073
6 0.023737 91.01041 2.386103 1.674290 4.929200
7 0.026313 88.11711 2.976382 2.326990 6.579520
8 0.028367 84.90036 3.376980 2.783734 8.938924
9 0.030475 81.38129 2.986563 3.496885 12.13526
10 0.032785 76.88578 2.630474 4.784743 15.69901
Variance Decomposition of LP:
Click “View” – “Variance
Decompositions” – “Table”

24
1 0.003904 0.057833 99.94217 0.000000 0.000000
2 0.006102 0.232518 99.30812 0.034317 0.425045
3 0.007787 0.493569 99.04644 0.076551 0.383441
4 0.009032 0.723986 98.88313 0.067843 0.325045
5 0.010067 1.013711 98.49578 0.206479 0.284028
6 0.010816 2.379293 96.86372 0.504991 0.251992
7 0.011544 4.710690 94.19444 0.867165 0.227708
8 0.012314 6.518148 91.82371 1.438480 0.219661
9 0.012968 7.566270 90.49069 1.743578 0.199466
10 0.013545 8.302143 89.10389 2.390148 0.203815
Variance Decomposition of LR:
1 0.072920 2.995915 0.019765 96.98432 0.000000
2 0.111546 3.619142 0.098381 96.28206 0.000418
3 0.139640 4.349874 0.076814 95.55480 0.018517
4 0.161746 4.672351 0.223168 95.05622 0.048258
5 0.176165 5.039088 0.224267 94.69537 0.041277
6 0.191569 5.355593 0.193439 94.34811 0.102858
7 0.208351 4.742339 0.306652 94.75085 0.200158
8 0.222819 4.361189 0.434910 94.95968 0.244217
9 0.236249 3.960742 0.732402 94.78659 0.520266
10 0.251486 3.503003 0.914070 94.85731 0.725617
Variance Decomposition of LY:
1 0.051559 0.724280 0.570742 0.577937 98.12704
2 0.060572 0.608491 0.768220 0.439926 98.18336
3 0.072073 0.473792 1.096219 0.640465 97.78952
4 0.082283 1.219285 1.277598 0.572537 96.93058
5 0.089036 1.136213 1.872747 0.548866 96.44217
6 0.094439 1.235009 1.895860 0.577269 96.29186
7 0.098761 1.619555 2.445372 0.530370 95.40470
8 0.104042 2.296307 4.431683 0.639905 92.63211
9 0.108643 2.798176 4.585921 1.005189 91.61071
10 0.112538 3.291952 5.643364 1.336476 89.72821
Cholesky Ordering: LM3 LP LR
LY

25
STEP 2.6: Impulseresponse functions(IRFs)
16. Estimate the impulse response functions (IRFs), click “Estimate” and change the “Vector
Error Correction” to “Unrestricted VAR” and increase one more lag for the model from
lag 12 to lag 13.
Select “Impulse”

26
-.010
-.005
.000
.005
.010
.015
1 2 3 4 5 6 7 8 9 10
Response of LM3 to LM3
-.010
-.005
.000
.005
.010
.015
1 2 3 4 5 6 7 8 9 10
Response of LM3 to LP
-.010
-.005
.000
.005
.010
.015
1 2 3 4 5 6 7 8 9 10
Response of LM3 to LR
-.010
-.005
.000
.005
.010
.015
1 2 3 4 5 6 7 8 9 10
Response of LM3 to LY
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of LP to LM3
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of LP to LP
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of LP to LR
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of LP to LY
-.04
.00
.04
.08
.12
1 2 3 4 5 6 7 8 9 10
Response of LR to LM3
-.04
.00
.04
.08
.12
1 2 3 4 5 6 7 8 9 10
Response of LR to LP
-.04
.00
.04
.08
.12
1 2 3 4 5 6 7 8 9 10
Response of LR to LR
-.04
.00
.04
.08
.12
1 2 3 4 5 6 7 8 9 10
Response of LR to LY
-.04
-.02
.00
.02
.04
.06
1 2 3 4 5 6 7 8 9 10
Response of LY to LM3
-.04
-.02
.00
.02
.04
.06
1 2 3 4 5 6 7 8 9 10
Response of LY to LP
-.04
-.02
.00
.02
.04
.06
1 2 3 4 5 6 7 8 9 10
Response of LY to LR
-.04
-.02
.00
.02
.04
.06
1 2 3 4 5 6 7 8 9 10
Response of LY to LY
Response to Cholesky One S.D. Innovations ± 2 S.E.

Time series analysis use E-views programer

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Time series analysis use E-views programer

Similar to Time series analysis use E-views programer (20)

Recently uploaded

Recently uploaded (20)

Time series analysis use E-views programer