Order Description
Use EVIEW, ONLY Do Q1-Q3, there is a sample, you can read, BUT do not copy
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Econometric Methods
FIN5EME Semester 2, 2016 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.
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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:
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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
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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
t jj
m
j t jtjt
t
m
j
t jj
m
j t jtjt
RD uRPeRD
RD uRPeRP
2
1
4
3
1 32 2 1
1
1
2
1 11 1 1
4
12
log loglog
log ;loglog
?? ?? ? ? ? ?? ? ? ? ?? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ?? ? ? ?? ? ?
.
where e represents the residual from the co-integrating regression.
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If you find the time series not to be co-integrated, estimate the following short-run model:
t
m
j
t jj
m
j t jtj
t
m
j
t jj
m
j t jtj
RD uRPRD
RD uRPRP
2
1
4
1 23
1
1
2
1 11
23
12
log loglog
log loglog
?? ?? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ?? ? ? ? ? ? ?? ? ?? ?
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 ß j ’s). You may conduct the t-test or F-test on ß j ’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.
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