Econometric Methods

Econometric Methods

Assignment 02
This assignment is worth 20% of the total mark and should be submitted by Monday 9pm of
Week 12 (17/10/2016) to the LMS by electronic submission.
This is a group based assignment with maximum 4 members in a group. Plagiarism will be
dealt with according to the University policy. Late submission will not be accepted and
no extensions will be given. This is a project where students should solve the questions
independently. The lecturer is not allowed to help you on any aspect of the assignment,
and will not answer any questions directly related to the assignment, unless they are for
clarification of the questions.
Your report should provide concise and relevant answers to all questions below and the
corresponding computer outputs. It does not need to follow a formal report format. The
computer outputs should be attached as an appendix to your report. In conducting
statistical tests throughout, clearly state all relevant information, such as the null and
alternative hypotheses, the distribution you use, the level of significance, the decision rule
(critical value or p-value).
Note that the “explain” or “interpret” type questions require concise and to-the-point
answers (no more than 0.5 A4 double-spaced page), but they should be relevant and
informative. Your report should be typed on A4 pages, double-spaced.
Part I: Data Details and Background (No Questions)
The file assign2.wf1 contains the US stock price (S&P 500, RP) and dividend (S&P 500, RD),
all adjusted with inflation, monthly from 1871 to 2014. The data is obtained from Robert
Shiller’s website (http://www.econ.yale.edu/~shiller/).
It is claimed that stock price is closely related with dividend in the short-run and long run.
The question as to whether the dividend has explanatory or predictive power for future
stock return is a contentious issue in finance. In this assignment, you will analyze the
relationship using the above-mentioned data set for the U.S. stock market. You may find a
section of Fabozzi book (page 199-205) useful for background and as an example of
statistical analysis on this topic.
Since the nature of the relationship can change over time (due to structural change;
institutional changes; regulatory changes, etc), it is sensible to break the data set into
different windows. This will also show us how the short-run and long-run relationships (if
they exist) have changed over time.
2
We break the whole data set into different windows; each covering a period of 20 years
(240 monthly observations) as below:
Data Set Number Period
0 1901:01 – 1920:12
1 1911:01 – 1930:12
2 1921:01 – 1940:12
3 1931:01 – 1950:12
4 1941:01 – 1960:12
5 1951:01 – 1970:12
6 1961:01 – 1980:12
7 1971:01 – 1990:12
8 1981:01 – 2000:12
9 1991:01 – 2010:12
You are assigned with the window which matches the last digit of your student ID. For
example, if the last digit of your ID is 5, you should use the data set 5 which covers the
period from 1951 – 1970.
If you use the wrong data set, your mark for this assignment will be 0.
In Eviews, you can set the data range,
by clicking Sample Button and writing the required sample range. Click OK, then you see
that the sample range is reset with 240 observations.
It is a usual convention to transform the data into natural log. This is to estimate the
elasticity and to stabilize the data by transforming the data into a smaller scale.
You can do this by clicking Genr button write the equation as below:
3
Click OK, then you will see that a new time series logRP is generated. Repeat the above to
generate logRD, as log-transformation of RD.
Note that, if you run the regression between logRP and logRD, the slope coefficient
represents the elasticity between the two. That is it should be interpreted as the percentage
change of RP with respect to 1% change of RD.
I suggest that you save your file at this stage by clicking the Save button
Part II: Analysis (Answer All Questions)
Question 1 [10 marks: 2 + 8] ? Report time plots and SACF of the time series in level (logRP and logRD).
? Based on these measures, provide a summary of the descriptive properties of these
time series in relation to their main components, dependence structure, and stylized
features of financial time series.
Question 2 [10 marks: 2 + 8] ? Report time plots and SACF of the time series in first difference (?logRP and
?logRD).
? Based on these measures, provide a summary of the descriptive properties of these
time series in relation to their main components, dependence structure, and stylized
features of financial time series.
Note: In Eviews, you can use d(X) to represent the first difference of X
4
Question 3 [10 marks: 5 + 5] ? Find the best fitting ARMA models for ?logRP and ?logRD, justifying your final
chosen models with appropriate statistical measures or tests.
? Using these models, generate dynamic (out-of-sample) forecasts for the next 12
month for ?logRP and ?logRD. Evaluate the accuracy of the forecasts using the
MAPE and Theil’s U.
Question 4 [10 marks: 5+5] Conduct the ADF test for logRP and logRD; and determine whether they are I(1) or I(0).
(Note: a test for second unit root is not necessary)
Question 5 [10 marks: 5+5] Regardless of your test outcomes in Question 4, let us assume that all of these time series
are of I(1).
Run the regression of logRP against logRD (including the intercept term).
? Conduct the test for cointegration using the ADF test
? Depending on the outcome of the test, interpret the long-run relationship implied
the regression results.
In Eviews, the residuals from a regression are stored in the variable called resid, after you
run the regression. Hence, straight after you run the regression, click Genr button and
write e = resid in the pop-up window before you click OK. Then, the residuals from the
regression are stored in the variable called e.
If you find the time series to be co-integrated in Question 5, estimate the following errorcorrection
model:
t
m
j
j t j
m
j
t t j t j
t
m
j
j t j
m
j
t t j t j
RD e RP RD u
RP e RP RD u
2
1
4
3
1
2 2 1 3
1
1
2
1
1 1 1 1
4
1 2
log log log
log log log ;
? ?
? ?
?
?
?
? ?
?
?
?
? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
.
where e represents the residual from the co-integrating regression.
5
If you find the time series not to be co-integrated, estimate the following short-run model:
t
m
j
j t j
m
j
t j t j
t
m
j
j t j
m
j
t j t j
RD RP RD u
RP RP RD u
2
1
4
1
2 3
1
1
2
1
1 1
3 2
1 2
log log log
log log log
? ?
? ?
?
?
?
?
?
?
?
?
? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ?
? ? ?
You may use an information criterion to determine the lag order values m1, m2, m3, and m4.
For simplicity, you may assume that m1= m2 = m3 = m4.
In Eviews, ?Xt-k can be represented as d(X(-k)); and Xt-k can be represented as X(-k) (k = 1,
2, 3, …).
Question 6 [20 marks] Interpret the estimation results of the above short-run models, paying attention to
? speed of adjustments to long-run equilibrium (if logRP and logRD are co-integrated);
and
? whether the past changes of RD have explanatory power (or predictive ability) for the
current change of RP.
? whether the past changes of RP have explanatory power (or predictive ability) for the
current change of RP.
Note: Interpret the estimated coefficients (the sum of ßj’s). You may conduct the t-test or
F-test on ßj’s to evaluate the statistical significance of the predictive ability of earnings or
dividend. For the F-test, the Wald test option in Eviews can be used.
Question 7 [10 marks] Provide a non-technical summary of your findings from Questions 1 to 6, in less than 200
words.
End of Document