The 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. In conducting statistical tests throughout, clearly state all relevant information, such as the null and alternative hypotheses, the distribution that has been used the level of significance and the decision rule (critical value or p-value). The report should be typed on A4 pages; the text should be double-spaced and in ‘Times New Roman’ font.

**The following two separate files should be submitted with clear identification of name, surname and student ID:**

(Hint: Save all files with the filename: “Assignment_FirstName_ID.***”)

- An Eviews file containing all estimated descriptive statistics and models.
- A written report not exceeding 1,000 words of the results of the required analysis.

# Data Details and Background (No Questions)

The file **assignment.wf1** contains the US stock price (S&P 500, RP) and dividend (S&P 500, RD), all adjusted for inflation, monthly from Jan 1871 to Mar 2018. The data are obtained from Robert Shiller’s website (http://www.econ.yale.edu/~shiller/).

Finance literature has documented relationship between stock price, earning, and dividend in the short-run and long run. The question whether the dividend, or earning has explanatory or predictive power for future stock returns is a contentious issue in finance. In this assignment, you will analyze the relationhip between stock price, earning and dividend in the short and long-run using the data mentioned above above set from the U.S. stock market. A section of Fabozzi et al. (2014, pp 199-205) is useful as a 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; policy changes, etc.), it is recommended to break the data set into different windows. This will also demonstrate how the short-run and long-run relationship (if it exists) has changed over time.

The data set is subdivided into different windows; each covering a period of 40 years (480 monthly observations) as below:

Data Set Number | Period |

0 | 1888:04 – 1928:03 |

1 | 1898:04 – 1938:03 |

2 | 1908:04 – 1948:03 |

3 | 1918:04 – 1958:03 |

4 | 1928:04 – 1968:03 |

5 | 1938:04 – 1978:03 |

6 | 1948:04 – 1988:03 |

7 | 1958:04 – 1998:03 |

8 | 1968:04 – 2008:03 |

9 | 1978:04 – 2018:03 |

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 1938 – 1978.

__If you use the wrong data set, your mark for this assignment will be 0.__

** **

It is usual to transform the data into a natural log. This procedure is necessary to estimate the elasticity and to stabilize the variance of the data by transforming them into a smaller scale. You can do this by clicking on the Genr Button and writing the equation as below:

Click OK, then you will see that a new time series logRP is generated. Repeat the above to generate logRD, logRE as log-transformation of RD, log-transformation of RE, respectively.

Note that, if you run the regression model of logRP on logRD, logRE, the slope coefficients represent the elasticity between the stock price and the explanatory variables (dividend and earning). For example, a slope coefficient on logRD should be interpreted as the percentage change of RP with respect to 1% change of RD or ** elasticity** of RP with respect to RD.

*You are suggested to save your file at this stage by clicking the Save Button. *

**Assignment **(Answer All Questions)

# Question 1 [Total 10 marks]

** **

** **

- a) Report the time plots and SACF of the time series in according to level series data (logRP, logRD, and logRE).

## [5 marks]

- b) 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.

**[5 marks] **

** **

# Question 2 [Total 10 marks]

** **

** **

- a) Report time plots and SACF of the time series in first difference (logRP, logRD, and logRE).

## [5 marks]

- b) 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.

**[5 marks] **

**Note: **In Eviews, you can use d(X) to represent the first difference of X.

Question 3 [Total 10 mark]

- a) Find the best fitting ARMA models for logRP, logRD, and logRE, justifying your final chosen models with appropriate statistical measures or tests.

## [6 marks]

- b) Using these models, generate dynamic (out-of-sample) forecasts for the next 12 month for logRP, logRD, and logRE. Evaluate the accuracy of the forecasts using the MAPE.

**[4 marks] **

** **Question 4 [Total 10 marks]

Conduct the ADF test for logRP, logRD, and logRE,; and determine whether they are I(2), or I(1), or I(0).

Question 5 [Total 10 marks]

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, and logRE (including the intercept term).
**marks]**

- Conduct the test for cointegration using the ADF test.
**marks]**

- Depending on the outcome of the test, interpret the long-run relationship implied by the regression results.

**[4 marks] **

**Notes:** In Eviews, the residuals from a regression are stored in the variable called resid, after you run the regression. Hence,

**, click Genr and write**

__straight after you run the regression__**e = resid**before you click OK. Then, the residuals from the regression are stored in the variable called

*e*. The critical values for the unit root test for the residuals are given in the lecture notes.

If you find the time series to be co-integrated in Question 5, estimate the following error correction model:

log𝑅𝑃𝑡 = 𝛼1 + 𝛾1𝑒𝑡−1 + 𝛽1∆log𝑅𝑃𝑡−1 + 𝛽2∆log𝑅𝐷𝑡−1 + 𝛽3∆log𝑅𝐸𝑡−1 + 𝑢1𝑡

∆log𝑅𝐷𝑡 = 𝛼2 + 𝛾2𝑒𝑡−1 + 𝛽4∆log𝑅𝑃𝑡−1 + 𝛽5∆log𝑅𝐷𝑡−1 + 𝛽6∆log𝑅𝐸𝑡−1 + 𝑢2𝑡

∆log𝑅𝐸𝑡 = 𝛼3 + 𝛾3𝑒𝑡−1 + 𝛽7∆log𝑅𝑃𝑡−1 + 𝛽8∆log𝑅𝐷𝑡−1 + 𝛽9∆log𝑅𝐸𝑡−1 + 𝑢3𝑡

where *e* represents the residual from the co-integrating regression.

If you find the time series not to be co-integrated, estimate the following short-run model:

∆log𝑅𝑃_{𝑡 }= 𝛼_{1 }+ 𝛽_{1}∆log𝑅𝑃_{𝑡−1 }+ 𝛽_{2}∆log𝑅𝐷_{𝑡−1 }+ 𝛽_{3}∆log𝑅𝐸_{𝑡−1 }+ 𝑢_{1𝑡}

∆log𝑅𝐷_{𝑡 }= 𝛼_{2 }+ 𝛽_{4}∆log𝑅𝑃_{𝑡−1 }+ 𝛽_{5}∆log𝑅𝐷_{𝑡−1 }+ 𝛽_{6}∆log𝑅𝐸_{𝑡−1 }+ 𝑢_{2𝑡}

∆log𝑅𝐸_{𝑡 }= 𝛼_{3 }+ 𝛽_{7}∆log𝑅𝑃_{𝑡−1 }+ 𝛽_{8}∆log𝑅𝐷_{𝑡−1 }+ 𝛽_{9}∆log𝑅𝐸_{𝑡−1 }+ 𝑢_{3𝑡}

In Eviews, *X*_{t-1 }is be represented as d(X(-1)); and *X*_{t-1} as X(-1).

# Question 6 [Total 10 marks]

** **

Interpret the estimation results of the above short-run models, paying attention to

- Speed of adjustments to long-run equilibrium (if logRP, logRD, and logRE are cointegrated);
**marks]**

- Whether the past changes of RD, and/or RE have explanatory power (or predictive ability) for the current change of RP;
**marks]**

- Whether the past changes of RP have explanatory power (or predictive ability) for the current change of RP.
**[2 marks]**

**Note: **Interpret the estimated coefficients and their economic significance and conduct the t-test on

*β*’s to evaluate the statistical significance.

_{j}# Question 7 [Total 10 marks]

Provide a non-technical summary of your findings from Questions 1 to 6, in less than 200 words. Your discussion should include how the current stock return is affected by the past values of dividend changes and/or stock return, economically and statistically.

# Reference List

Fabozzi, F.J., Focardi, S. M., Rachev, S. T., Arshanapalli, B. G. (2014). The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications (Frank J. Fabozzi Series). Somerset: Wiley.