LAB# 06
Exercise#12.4
The data file contain oil.dat contains 88 annual observations on the price of oil(in 1967 constant
dollars) for the period 1883-1970.
(a)Plot the data.Do the data look stationary,or nonstationary?
(b)Use a unit root test to demonstrate that the series is stationary?
(c)What do you conclude about the order of integration of this series?
Part (a):
oil
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
10 20 30 40 50 60 70 80
Comment: Series is not stationary in mean and variance,trend is also present in it.
Part (b): Load the data in eviews the click on Quick →Series statistics→unit root test→series name oil
Null Hypothesis: D(OIL) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 3 (Automatic - based on SIC, maxlag=11)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.073091 0.0004
Test critical values: 1% level -4.072415
5% level -3.464865
10% level -3.158974
*MacKinnon (1996) one-sided p-values.
Test Of Hypothesis:
Ho:Series is stationary
H1:Series is not stationary
Dickey Fuller Test Statistics:
-5.073091 →from table
Yt=β1+β2+€t
At 1%
-4.072415>-5.073091
At 5%
-3.464865>-5.073091
At 10%
-3.158974>-5.073091
Conclusion:At 1%,5% and 10% level of significance ,there is evidence that series is non stationay and p-
value less than 0.05 it means we will reject null hypothesis so,series is non stationary.
Exercise#12.11
The data file mexico.dat contain real GDP for mexican and the US from the first quarter of 1980 to the
third quarter of 2006.Both series have been standardized so that the average value in 2000 is 100.
Solution: Plot mexico and usa in eviews after loading the data.
120
110
100
90
80
70
60
50
10 20 30 40 50 60 70 80 90 100
mexico usa
Comments: Series are moving together so they are co-integrated.
Command:
ls mexico c usa
genr t=resid
plot t
Result:
T
10.0
7.5
5.0
2.5
0.0
-2.5
-5.0
-7.5
-10.0
10 20 30 40 50 60 70 80 90 100
Comment: Series of residuals having no intercepts as well as no trend.
Now click on Quick →Series statistics→unit root test→series name t
Result:
Null Hypothesis: T has a unit root
Exogenous: None
Lag Length: 4 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.892826 0.0042
Test critical values: 1% level -2.587831
5% level -1.944006
10% level -1.614656
*MacKinnon (1996) one-sided p-values.
Test Of Hypothesis:
Ho:Series are co-integrated.
H1:Series are not co-integrated.
Dickey Fuller Test Statistics:
-2.892826 →from table
Yt=βXt+€t
At 1%
-2.587831>-2.892826(reject Ho)
At 5%
-1.944006>-2.892826(reject Ho)
At 10%
-1.614656>-2.892826(reject Ho)
Conclusion:
Since p-value is less than 0.05 it means we reject our null hypothesis so,the series are not co-integrated.
For the 1st difference:
Null Hypothesis: D(T) has a unit root
Exogenous: None
Lag Length: 3 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.972760 0.0001
Test critical values: 1% level -2.587831
5% level -1.944006
10% level -1.614656
*MacKinnon (1996) one-sided p-values.
Test Of Hypothesis:
Ho:Series are co-integrated.
H1:Series are not co-integrated.
α=0.05
Dickey Fuller Test Statistics:
-3.972760 →from table
Yt=βXt+€t
At 1%
-2.587831>-3.972760 (reject Ho)
At 5%
-1.944006>-3.972760 (reject Ho)
At 10%
-1.614656>-3.972760 (reject Ho)
Conclusion:
Since p-value is less than 0.05 critical values are greater than t-statistics so we reject our null
hypothesis.It means the series are not co-integrated.
Example 1:Fitting a GARCH model to stock data by using E1032 file from ITSM
Open ITSM and load data E1032 then select transform→subtact mean,following graph will appear.
Series
6.
4.
2.
0.
-2.
-4.
-6.
-8.
0 50 100 150 200 250 300 350 400 450
==========
ITSM::(INFO)
==========
# of Data Points = 464
Subtracted Mean = .0608
Sample Variance = 1.531766
Std.Error(Sample Mean) = .049140
(square root of (1/n)SUM{(1-|h|/r)acvf(h)}, |h|<r=[sqrt(n)])
MODEL:
ARMA Model:
X(t) = Z(t)
WN Variance = 1.000000
Garch Model for Z(t):
Z(t) = sqrt(h(t)) e(t)
h(t) = 1.000000
{e(t)} is IID N(0,1)
Click on GARCH icon and put value of alpha as 1 and beta as 1 also and select use normal noise option.
Then click on MLE icon and click ok.
========================================
ITSM::(Garch Maximum likelihood estimates)
========================================
ARMA Model:
X(t) = Z(t)
Garch Model for Z(t):
Z(t) = sqrt(h(t)) e(t)
h(t) = .1288447 + .1352892 Z^2(t-1)
+ .7853676 h(t-1)
Alpha Coefficients
.128845 .135289
Standard Error of Alpha Coefficients
.048701 .020201
Beta Coefficients
.785368
Standard Error of Beta Coefficients
.040705
AICC(Garch) = .146906E+04
-2Log(Likelihood) = .145783E+04
Accuracy parameter = .0008000000
Number of iterations = 13
Number of function evaluations = 120
Optimization stopped within accuracy level.
