MATH5315M Applied Statistics and Probability
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MATH5315M Applied Statistics and Probability
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 bus.txt contains the waiting time in minutes (recorded to several decimal places).
Draw a histogram and a boxplot for these data. Try different break points for the histogram (see the help pages), and conclude that the waiting times Y can be modelled as Y = X +a, in which X has a exponential or gamma distribution. What do you think would be a good choice for a?
Find the maximum likelihood estimate of a (requires mostly mathematical calculations, rather than R commands). Use your value to obtain the possible X values (by subtrac- tion).
Fit an exponential distribution and a gamma distribution to the shifted waiting times (X) using the method of moments. Write a report that briefly explains why the expo- nential distribution might be an appropriate distribution for these times and 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. (Any calculations or output from a statistical package should be added as an appendix.)
(9 out of 30 marks, no more than 3 sides of A4)
3. The file deaths.csv contains the UK government’s official total number of weekly deaths of those who previously tested positive with COVID-19. Find a suitable time series model for this dataset, and use it to predict the following two weeks, with corre- sponding 95% confidence intervals for your prediction. Repeat the task using the square root of the data, but back-transforming the forecast (and intervals) to the original scale. Interpret your model, and state, with reasons which model you prefer.
The file xall.csv contains a subset of the above data, but also includes a column of the total number of weekly COVID-19 cases (as determined by a positive test). Find a suitable model which enables a prediction of the number of deaths in each week, using information (in this file) from previous weeks. Specifically try to model the number of deaths in the weeks ending 2020-08-07 to 2021-01-29 (inclusive) and use your model to predict the number of deaths in the week ending 2021-02-05. Discuss the validity of the assumptions made by your model.
For all parts of this question, any calculations or output from a statistical package should be added as an appendix.
(12 out of 30 marks, no more than 4 sides of A4)
4. The data file USD-GBP.csv contains the Forex daily close data for the USD to GBP exchange for a twelve year period. For the final part of this question, use appropriate time series models to investigate the change in volatility in the exchange rate before and after the credit crisis (for simplicity, you can assume that the credit crisis struck overnight between 31st July 2007 and 1st August 2007).
Write a report on the changing volatility over this period, which includes your fitted models and any analysis of underlying model assumptions that you may have made. Once again, any calculations or output from a statistical package should be added as an appendix.
(9 out of 30 marks, no more than 3 sides of A4)
All of the data files that are needed to answer the questions are available from the modules page on the Minerva website. There is no word count for this assignment, but
you are limited to 10 sides of A4 paper (not including any appendices). The deadline date for this assignment is 12.00 noon on 9th December 2021.
An electronic copy of the assignment must be submitted to the Assignment Submission area within the module resource on Minerva no later than 12 noon on the deadline date.
Failure to meet this initial deadline will result in a reduction of marks. Faxed, emailed or hard copies of the assignment will not be accepted. Please ensure that the file name is saved as your student ID e.g. (212345678.pdf) and your name is not written anywhere on your assignment.
2021-12-13