Diagnostic Tests carried out on the data included the normality test,
stationary test, Multicolinearity test,
serial correlation test and the structural stability test.
Normality is a condition in which the used variables follow the standard
A normally distributed data set has a probability density.
Test use for normality:-
Jarque-Bera test of normality .this test first computes the skewness(s) and
kurtosis(k) and uses the following statistics;
JB = N [S2
/6 + (K-3)2
The Jarque-Bera test is based on the sample skewness and sample kurtosis.
with S, K, and N denoting the sample skewness, the sample kurtosis, and the
sample size, respectively.
Method 0f Normality test:-
Check the series normal distribute we apply Jarque-bera test
The following Steps are adopted in E-view
Open E-view create a new work file and open any data file like
Paste the question in empty group.
Go to option view (where paste the data) and select Descriptive stat than
common sample and press ok.
We will get the result.
Table show the result that data is
normally distribute or not
LPGDP LCPI LINV
Mean 4.146104 1.781789 0.969416
Median 4.145150 1.801283 0.968722
Maximum 4.961491 2.352240 1.196225
Minimum 3.392548 1.238794 0.699115
Std. Dev. 0.455947 0.319540 0.115272
Skewness 0.082936 0.001676 0.013718
Kurtosis 1.840198 1.810464 3.081233
Jarque-Bera 1.830206 1.886676 0.009802
Probability 0.400475 0.389326 0.995111
Sum 132.6753 57.01725 31.02132
Sum Sq. Dev. 6.444524 3.165285 0.411919
Observations 32 32 32
Ho=series is normal distributed.
H1=series is not normal distributed.
NOTE: If probability of normative statistic is less than 0.05, it is not normal
distribution. If probability of normative statistic is greater than 0.05, it is
Like (p ≤ 0.05), (p ≥ 0.05)
SO:-we accepted the Ho that shows lpgdp , lcpi., linv,is normally
stationary process reverts around a contsant long –term mean
and has a constant variance independent of time.
A stationary process has the property that the mean , variance
and auto-correlation structure don’t change over the time.
The stationary series :-
If a time-series is stationary its mean, variance and auto
co-variance remains the same no matter what point we measure them i.e.
they are time invariant.
Test used for Stationary
Standard inference procedures do not apply to regressions which contain
an integrated dependent variable or integrated regressors. Therefore, it is
important to check whether a series is stationary or not before using it in a
regression. The formal method to test the Stationarity of a series is the unit
1:The Dickey-Fuller (DF) Test
2:The Augmented Dickey-Fuller Test (ADF)
3:The Phillips-Peron (PP) Test
A non stationary time series will have a time-varying mean and
time-varying variance or both.
Non-stationary behavior can be trends , cycles, random walks.
Check the series is Stationary or Non-
The following steps are adopted in Eviews.
Open Eviews and create a new work file .
Go to quick option select empty group.
Open any data file like(male , female, salary and spending).
And paste in empty group in Eviews.
Step 2 :
Reopen back file and select any variable and double click on it and see
new file. Go to view of this file click the unit-root test press OK.
New window will open and select level and also trend & intercept press
Check the Results
Null Hypothesis: FEMALES has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic based on SIC, MAXLAG=5)
Augmented Dickey-Fuller test statistic -0.403705 0.9809
Test critical values: 1% level -4.416345
5% level -3.622033
10% level -3.248592
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(FEMALES)
Method: Least Squares
Date: 05/24/14 Time: 14:06
Sample (adjusted): 1968 1990
Included observations: 23 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
FEMALES(-1) -0.035447 0.087804 -0.403705 0.6907
C 13.84571 40.77848 0.339535 0.7377
@TREND(1967) 0.142634 0.121177 1.177076 0.2530
R-squared 0.154234 Mean dependent var -0.521739
Adjusted R-squared 0.069657 S.D. dependent var 3.072896
S.E. of regression 2.963939 Akaike info criterion 5.132023
Sum squared resid 175.6987 Schwarz criterion 5.280131
Log likelihood -56.01826 Hannan-Quinn criter. 5.169272
F-statistic 1.823602 Durbin-Watson stat 1.675355
If answer are negative, it means stationary is right. If answer are positive, it
means stationary is wrong. If wrong then go to 1st
difference, also wrong then
go to 2nd
So the female series is stationary.
Multicollinearity is a problem in regression analysis that occurs when two
independent variables are highly correlated, e.g. r = 0.90, or higher.
In other words :
This problem occurs when the explanatory variables are very highly
correlated with each other.
Check the multicolinearity’s problem
i.Open E-view and also open question (1972- 2010).
ii.In E-view go option file ͢ work file ͢ enter start and end date ͢ press ok.
iii.Go to option Quick empty file paste the data.͢ ͢
i.Write command on command bar
genr dINF=INF-INF(-1) and press ok.
i.Double click on back window (dinf) select option view descriptive statistic stat͢ ͢ ͢
histogram. New diagram’s window will open.
ii.Go option Quick group statistic correlation new window will open. In this window͢ ͢
write variables and press ok.
If 0.05 less ͢
normality is not. If 0.05 above normality is exist.͢
If 50% above then there
is high multucolinarity. If 1% then there is prefect multicolinarity. If 50% less
then less multicolinarity.
So, there is perfect Multicolinearity exist among variables.