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How to write the project assignment? (an example)
Time series data – example CAMP
Unit-root testing. Why is it important?
Model adequacy: Serial correlation and heteroscedasticity tests
EViews illustrations
Course: Applied Econometrics
Instructor: S. Tashpulatov
• Introduction. You introduce from which area of economics your
research is about? For example, is it education economics or labor
economics? You also provide an explanation why your research
could be important and interesting.
• Data description. Here you list all variables and their description.
You also need to provide at least two types of plots: 1) histogram
(comment if your distribution plot is symmetric or asymmetric),
2) x y scatter plot (comment if the trend is increasing or decreasing).
• Economic relationship. Here you specify dependent and
explanatory variables. Also you provide a correlation matrix
including p-values. Avoid multicollinearity problem among your
explanatory variables.
2
How to write the project assignment?
• Methodology. Based on the correlation analysis specify a multiple
regression model. Your model should have at least two factors (i.e.,
explanatory variables).
• Estimation. Here you provide estimation results from Excel or
EViews. Also conduct Ramsey’s RESET test for model
specification (make sure to specify H
0
and H
1
in your project).
For this purpose, you need to create and save the fitted values of y
according to the model in H
0
.
• Statistical inference. Conduct hypothesis testing regarding the
significance of estimated model parameters (make sure to specify
H
0
and H
1
for each model parameter in your project).
3
How to write the project assignment?
• Goodness of fit test. Conduct the significance test of the overall
model (make sure to specify H
0
and H
1
in your project).
• Economic verification. Explain if the signs of estimated model
parameters correspond to economic intuition.
• Interpretation. Provide an interpretation of the estimated
parameters. Also provide an interpretation of the R-squared
(coefficient of determination).
• Conclusion. Here you need to summarize the major finding and
conclusion of your project.
• Bibliography. List at least two statistical sources.
4
How to write the project assignment?
Time series data: Real US oil prices to refineries
5
6
How to test the unit-root hypothesis?
• Augmented Dickey-Fuller test (known as ADF test)
available in EViews
H
0
: time series contains unit root (i.e., nonstationary)
H
1
: time series does not contain unit root (i.e., stationary)
Decision to reject H
0
is based on the p-value of test.
Remark: p-value in EViews is denoted by Prob.
8
ADF test results
Conclusion: Because the p-value is greater than 10%, we are not in the
tail. Therefore, we do not reject H
0
and conclude that the time series is
nonstationary. See Table 2 on page 5 in the article.
9
Why is it important to test for
stationarity?
Many modeling techniques like ACF, PACF, Fourier Transform are
applicable ONLY for stationary time series. See Section 5.1 on page 5.
What can be done if time series is nonstationary?
Many options. Depends on the case/purpose of your analysis. Ask for
recommendation from your supervisor or expert in time series
econometrics and your research area:
1) Include the time trend (linear, quadratic): a+bt+ct
2
2) Apply level differencing (working with changes)
3) Apply log differencing (working with relative changes, growth rate)
10
Modeling the dynamics of a stationary
time series
Significant results in the ACF and PACF plots can suggest which lags
should be included. We analyze the dynamics of the growth rate of
investment per capita.
Consider the model: ,where
is the growth
rate of investment per capita, which was tested before for stationarity.
t
t
t
u
y
y
3
3
0
t
y
12
Judging if the chosen specification in
your modeling is adequate
Use the ACF and PACF to check if your model is adequate. It is
important to analyze not only residuals but also squared residuals.
13
Correlogram of residuals (serial correlation test)
The model is good if the p-values are greater than 10%.
See Figure 6 on page 8 in the article.
14
Correlogram of squared residuals
(heteroscedasticity test)
The model is good if the p-values are greater than 10%.
See Figure 6 on page 8 in the article.
Estimating CAPM model
You are given monthly data on stock returns of the Delta US airline company
between 1978 and 1987.
15
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X
0.491783
0.119438
4.117469
0.0001
R-squared
0.122443
Mean dependent var
0.004853
Adjusted R-squared
0.122443 S.D. dependent var
0.095941
S.E. of regression
0.089876 Akaike info criterion
-1.972472
Sum squared resid
0.961246 Schwarz criterion
-1.949243
Log likelihood
119.3483 Hannan-Quinn criter.
-1.963039
Durbin-Watson stat
1.987114
Dependent Variable: Y
Method: Least Squares
Sample: 1 120
Included observations: 120
free
Risk
t
Market
t
Delta
free
Risk
t
Delta
t
R
R
R
R
u
x
y
Model verification: residual analysis
16
Model verification: autocorrelation test
for times series data. CAPM
17
Sample: 1 120
Included observations: 120
Correlogram of Residuals
Autocorrelation
Partial Correlation
AC
PAC
Q-Stat
Prob
1
0.003
0.003
0.0009
0.977
2 -0.012 -0.012
0.0183
0.991
3 -0.074 -0.074
0.7039
0.872
4
0.048
0.049
0.9965
0.910
5 -0.106 -0.109
2.4383
0.786
6 -0.110 -0.115
4.0052
0.676
Model verification: heteroskedasticity test
for times series data. CAPM
18
Sample: 1 120
Correlogram of Residuals Squared
Included observations: 120
Autocorrelation
Partial Correlation
AC
PAC
Q-Stat
Prob
1
-0.067
-0.067
0.5573
0.455
2 -0.013 -0.017
0.5770
0.749
3 -0.117 -0.120
2.3023
0.512
4
0.058
0.042
2.7232
0.605
5
0.064
0.068
3.2512
0.661
6 -0.104 -0.110
4.6503
0.589
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