How it worksΒΆ
The FTT algorithm consists of the following 9 steps.
- The loss data are sorted in descending order \(x_1 \geq x_2 \geq \ldots \geq x_n\) .
- Starting with the largest losses \(x_1, x_2\) (k = 2) the generalized Pareto distribution \(\hat{F}(x)\) (= Estimation) is adapted to the data.
- With this distribution the measure of deviation \(AU^2_k\) is calculated.
- Then the next smaller loss is added \((k \rightarrow k + 1)\) and the parameters of the generalized Pareto distribution are re-estimated.
- It continues with point (3) until the last loss value has been processed \((k = n)\).
- Depending on \(k\), a time series of the deviation measure results: \(AU^2_k\).
- The minimal deviation at a particular \(k^* \in [1, n]\) indicates the best fit of a model for the tail to the given loss data and the associated \(x_{k^*}\) corresponds to the sought threshold u.
- To assess the result, the confidence level is determined. (This describes how large the likelihood of a wrong decision would be, if the adapted distribution and thus the decision for the threshold were rejected)
- For further assurance, the statistics of the standard goodness-of-fit test (CM and AD test) are evaluated.
Note
- FTT strictly separates the procedure for detecting the threshold and the goodness of fit to evaluate the quality of the fit.
- There is no need for any external parameters, all information are gained form the data alone.