1. Topics of Advanced Econometrics
Dr Maqbool Sail
Presented By: Ayesha Siddiqa
F2021330005
PhD Economics
University of Management and Technology
Lahore
2. Two ways in general.
First is informal, done through graphs, and therefore called
graphical method.
Second is through formal tests or Numerical Method for
autocorrelation, such as:
1. Durbin Watson test
2. Breusch-Godfrey test
Applied Econometrics
Detecting Autocorrelation
3. Applied Econometrics
Graphical Method
.
Take the following series (quarterly data
from 1985q1 to 1994q2):
lcons = the consumer’s expenditure on food
ldisp = disposable income
lprice = the relative price index of food
Typing the following command in Eviews :
ls lcons c ldisp lprice
gives the regression results
4. Applied Econometrics
Graphical Method
Then we can store the residuals of this regression in a
vector by typing the command: genr res01=resid
And a plot of the residuals can be obtained with:
plot res01
While a scatter of the residuals against their lagged ter
ms can be obtained by: scat res01(-1) res01
14. Applied Econometrics
Result Interpretation
Graphical method is known as time sequence plot.
We take time (x axis) and estimated error term (y axis).
if error term follow visible pattern in particular time
period then show present autocorrelation.
Graphical Method
15. Applied Econometrics
Durbin Watson Test
The following assumptions should be satisfied:
The regression model includes a constant
Autocorrelation is assumed to be of first-order only
The equation does not include a lagged dependent
variable as explanatory variable
If its value is between 1.75 to 2.25 there is no autocorrel
ation. The value nearest to 2 the less will be the autocorr
elation.
16. Applied Econometrics
Durbin Watson Test
Step 1: Estimate model by OLS and obtain the residuals
Step 2: Calculate DW statistic
Step 3: Conclude
17. Applied Econometrics
Durbin Watson Test
Drawbacks of the DW test:
May give inconclusive results
Not applicable when a lagged dependent variable is
used
Can’t take into account higher order of autocorrelation
19. Applied Econometrics
Durbin Watson Test
Result Interpretation
The Durban Watson statistic will always assume a value
between 0 and 4.
A value of DW=2 indicate that there is no autocorrelation.
When the value is below 2 it indicates a positive autocorrela
tion.
A value higher than 2 indicates a negative serial correlation.
20. Applied Econometrics
Breusch-Godfrey Test
A Lagrange Multiplier test that resolves the drawbacks of th
e DW test.
Consider the model:
where:
1 2 2 3 3 4 4 ...
t t t t k kt
Y X X X X u
1 1 2 2 3 3 ...
t t t t t t
u u u u u e
21. Applied Econometrics
Breusch-Godfrey Test
It is a general test for at any order autocorrelation could be
tested. F & p- values are the decision criterias of autocorrel
ation.
= There is no autocorrelation
= There is autocorrelation
0
1
22. Applied Econometrics
Breusch-Godfrey Test
Step 1: Estimate model and obtain the residuals
Step 2: Run full LM model with the number of lags used bei
ng determined by the assumed order of autocorrelation
Step 3: Conclude
25. Applied Econometrics
Breusch-Godfrey Test
Result Interpretation
If the calculated p-value is higher than 0.05% level of sig
nificance, in that case the accepted, showing that autoc
orrelation subsist.
On the other hand, calculated p-value is lower than 0.05
% level of significance, the rejected, concluding that aut
ocorrelation problem present.
