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AS3015 ExTREME EvENT STATIsTIcs

2022-23

Coursework 2

● This coursework consists in preparing a report on the estimation of an extreme value model to some data set, using the statistical software R.

● The choice of the data set and the extreme value model (block maxima or peak over threshold) is left to the student.

Details on the report preparation and the choice of the data set follow.

1. The report should

(a) be in the range 2000-3000 words, excluding tables, ﬁgures and

equations, code;

(b) include information on the data set chosen (source, nature of the

data, basic summary statistics, . . . );

(c) explain the selected extreme value approach and the choice of the block size (in the block maxima approach) or the threshold (in the peak over threshold approach);

(d) extract as much information as possible from the estimated model: conﬁdence intervals, diagnostic plots, nature of the estimated model (tail behaviour, bounds), calculation of a return level with conﬁ- dence interval using the delta method, proﬁle log-likelihood plots, likelihood ratio test, . . . ;

(e) comment extensively on the results obtained in (d);

(f) include the R code used.

2. The R software can be downloaded at http://cran.r-project.org/. See the accompanying pdf document that explains how to estimate extreme value models with R. I also make available the R notes written by A. Tsanakas and R. Cowell.

3. The following are examples of resources that could be used to choose a data set (students are free to choose their own data from other sources

- the use of original data is appreciated!)

● Financial/economic data:

https://fred.stlouisfed.org/ (free, easily downloadable data sets)

http://finance.yahoo.com/

https://www.google.com/finance

http://www.nber.org/data/ (economics data and much more)

● National statistical oﬃces such as

http://www.ons.gov.uk/,

https://www .statcan .gc .ca/eng/start ,

http://ec .europa .eu/eurostat

● earthquake resources: