Empirical example about estimation of multivariate elliptical extreme quantile regions in a financial context. Data consists of three time series of market price indices from 2.7.2001 to 29.6.2007:

• Standard and Poors S&P 500,
• Financial Times Stock Exchange FTSE 100 and
• Nikkei 225.

We compute returns $Y_t = \log(X_{t+1} / X_t)$ and fit $\mathrm{EGARCH}(1, 1)$ model to time series of returns for each index. Then we use innovations for computing extreme quantile regions for several probabilities $p\in(1/2000, 1/5000, 1/10000)$.

1. Clone or unzip the repository.

   git clone https://github.com/perej1/elliptical-empirical.git
   

2. Install required packages by running the following R command in the project's root folder (R package renv has to be installed).

   renv::restore()
   

Emprical example involves three steps:

1. modify.R - Fitting of $\mathrm{EGARCH}(1, 1)$ models and computation of innovations.

2. test-assumptions.R - Test assumptions of independence, ellipticity and regular variation.

3. analyze.R - Estimation of extreme quantile regions.

Lastly, the script main.R is responsible for argument parsing. In order to perform all the three parts of the empirical example, just run the following.

Rscript main.R

If you wish to skip some parts of the empirical example, you can run something like below.

Rscript main.R --modify TRUE --test FALSE --analyze TRUE

That is, above snippet of code skips statistical tests.