Quantitative methods in accounting and finance: coursework assignment with groups exercise
2024/25
Brief
There are three. Please answer all questions. The number of marks for each sub-question is given in brackets. Though this is a group coursework exercise each student is expected to have an individual submission.
1. The data in Table 1 links the proportion of sales vouchers redeemed Y to the size of the dis- count ofered X .
|
Discount X
|
sample size
|
Number of coupons redeemed
|
Proportion of coupons redeemed Y
|
|
5
|
500
|
100
|
0.2
|
|
7
|
500
|
122
|
0.224
|
|
9
|
500
|
147
|
0.294
|
|
11
|
500
|
176
|
0.352
|
|
13
|
500
|
211
|
0.422
|
|
15
|
500
|
244
|
0.488
|
|
17
|
500
|
277
|
0.554
|
|
19
|
500
|
310
|
0.620
|
|
21
|
500
|
343
|
0.686
|
|
23
|
500
|
372
|
0.744
|
|
25
|
500
|
391
|
0.782
|
Table 1: Data for Question 1.
(a) Enter the data in Table 1 into R and list the commands used. [4 marks]
(b) Fit a linear regression model for Y. List the R commands used and give the table of t- statistics obtained. [4 marks]
(c) Interpret the R2 and t-statistics obtained in part (b). [4 marks]
(d) List the modelling assumptions for the classical normal linear regression model. [5 marks]
(e) Does the regression model in part (b) satisfy these regression modelling assumptions? Give reasons for your answer. [5 marks]
(f) If X = 15, X = -1 and X = 32 use the regression model obtained in part (b) to estimate the corresponding value of Y. Comment on the results obtained. [7 marks]
(g) Using R produce a 95% prediction interval for Y for each of the X-values in part (f). What is the interpretation of the prediction intervals in this case? [7 marks]
(h) Suggest two ways of improving the above analysis. [4 marks]
2. (a) Collect at least 2 years of daily price data for a financial asset of your choice. Example data sources include bloomberg, yahoo finance or cryptocurrency data from the website coinmarketcap .com Explain why the asset you have chosen is interesting and give the dates for which you have collected data. [2 marks]
(b) List the dates and data series collected by one of your classmates in part (a). [2 marks]
(c) List the dates and data series collected by another of your classmates in part (a). [2 marks]
(d) Explain some of the reasons for diferences in the data collected in parts (a-c). [5 marks]
(e) Calculate the log-returns for the data collected in part (a) and list the R code used. [2 marks]
(f) Calculate summary statistics (minimum, maximum, median, mean, standard deviation,
skewness and kurtosis) for the log-returns series in part (e) and list the R code used. Present the results in a table. [3 marks]
(g) Give a table of summary statistics corresponding to the log-returns for the dataset in part (b). [2 marks]
(h) Give a table of summary statistics corresponding to the log-returns for the dataset in part (c). [2 marks]
(i) Using the steps outlined in Lecture 9 verify the stylised empirical facts of financial time series for the data collected in part (a). [10 marks]
(j) Using the steps outlined in Lecture 10 fit an appropriate GARCH model to the log-returns series in part (e). [6 marks]
(k) Using the R package rugarch what are the two main ways of modifying standard GARCH models. [No additional R codes or commands are needed for this question]. [4 marks]
3. Critically reflect upon the groupwork components of Question 2. [20 marks]