This question paper consists of 2
printed pages, each of which is
identified by the reference MATH5315M.
Assessed coursework for the degree of
MSc Actuarial Finance
MSc Financial Mathematics
MATH5315M Applied Statistics and Probability
Assignment (worth 30% of the module mark)
This assignment consists of 2 pages and 4 main questions.
Hand-out date: Tuesday 5
th November 2019.
Hand-in date: Thursday 12th December 2019.
1. For the last 100 days a student has been collecting data on the number of minutes she
has to wait before her bus arrives at the Parkinson Building. The data file BusData.txt,
that you can find in Minerva, contains the waiting time in minutes (recorded to several
Fit an exponential distribution and a gamma distribution to the waiting times using
the method of moments. Write a report that compares the two fitted distributions with
the sample data. As part of the report, provide some plots that highlight the differences
between the fitted distributions and their level of their agreement with the sample data,
choosing the best one. If you are told that the arrival of buses follows a Poisson process,
which distribution would you expect to observe? (Any calculations or output from a
statistical package should be added as an appendix.)
(7 out of 30 marks, no more than 2 sides of A4)
2. The file StaffTurnover.txt contains information on staff turnover and net income per
employee for 56 NASDAQ listed companies. It is thought that net income per employee
is strongly dependent on staff turnover from the previous year. Use the 2012 net income
figures and the 2011 staff turnover figures to investigate the relationship using a normal
Write a report that covers the regression analysis, any assumptions that were made
(and their suitability) and the results of your analysis. As part of the report, provide
a plot that highlights the relationship and any plots you use to assess the validity of
assumptions. Consider if transforming somehow the data might lead to better results.
(Again, any calculations or output from a statistical package should be added as an
(8 out of 30 marks, no more than 4 sides of A4)
3. The file EuroIndices.txt in Minerva contains daily information for four stock indices
over a 150-trading-day period. First, attempt to fit the best three AR(p), ARMA(p, q)
and ARIMA(p, d = 2, q) models that you can obtain to the DAX data (in this question,
we will focus on the index value at the close of the trading day). Using appropriate
criteria, comment on which model is the best fit to the data. Also, using your selected
model, produce estimates for the DAX index over the next 10 trading days after the
period for which you have data.
For the second part of this question, fit an appropriate vector autoregressive model to
all four indices simultaneously. Consider the value of using of all the data in the context
of estimating the DAX index over the next 10 trading days.
Report on your findings for all parts of the question including any analysis of underlying model assumptions that you may have made. For all parts of this question, any
calculations or output from a statistical package should be added as an appendix.
(9 out of 30 marks, no more than 5 sides of A4)
4. You are asked to fit an ARIMA(p, d, q) model to the timeseries in the file Question4.txt,
which is available in Minerva. Attempt to fit the best ARIMA model that you can, commenting on assumptions made and the results obtained. Do you think this model is
appropriate? If it is, explain why you think so. If it is not, try to fit a different model.
For the second part of this question, predict 10 steps ahead by using the best model
that you found, and comment on the results.
(6 out of 30 marks, no more than 3 sides of A4)
All data files that are needed to answer these questions are available in Minerva. There
is no word count for this assignment, but you are limited to 14 sides of A4 paper
(not including any appendices).
The deadline date for this assignment is 16.00 on Thursday 12th December 2019.
A hard copy of the assignment must be submitted to my pigeonhole by 4pm
on the deadline date. My pigeonhole is located in the School of Mathematics, Level
8, around the MALLs area. Ask at the Taught Student Office if you can not find it.
Faxed or emailed copies of the assignment will not be accepted.
Failure to meet this initial deadline will result in a reduction of marks, you can ask your
lecturer for more details about this.
NAME: Please staple all the pages together and clearly write your name and student ID on every page of your assignment.