# tdc: Tail Dependence Coefficient In FRAPO: Financial Risk Modelling and Portfolio Optimisation with R

## Description

This function returns the pairwise tail dependence coefficients between N series. The TDCs are estimated non-parametrically by either the empirical tail copula or based on the stable tail-dependence function.

## Usage

 `1` ```tdc(x, method = c("EmpTC", "EVT"), lower = TRUE, k = NULL, ...) ```

## Arguments

 `x` Matrix, or an object that can be coerced to it. `method` Character, the type of non-parametric estimation. `lower` Logical, if `TRUE` (default), lower TDC are computed and upper TDC, else. `k` Integer, the threshold value for the order statistic. If left `NULL`, then `k = sqrt(nrow(x))` is used. `...` Ellipsis, arguments are passed down to `rank`.

## Details

For a matrix or an object that can be coerced to it with ```ncol(x) >= 2```, the pair wise tail dependencies are estimated non-parametrically and returned as a symmetric matrix. The threshold value `k` is the upper/lower bound for the order statistics to be considered. The diagonal elements are always equal to one, because a series has a dependence of one with itself, of course.

## Value

A matrix with the tail dependent coefficients.

Bernhard Pfaff

## References

Schmidt, R. and Stadtm\"uller, U., Nonparametric estimation of tail dependence, The Scandinavian Journal of Statistics, 33, 307–335.

`PMTD`

## Examples

 ```1 2 3 4 5``` ```data(StockIndex) Rets <- returnseries(StockIndex, method = "discrete", trim = TRUE, percentage = TRUE) tdc(Rets, method = "EmpTC") tdc(Rets, method = "EVT") ```

### Example output

```Loading required package: cccp
Using the GLPK callable library version 4.52
Financial Risk Modelling and Portfolio Optimisation with R (version 0.4-1)

SP500      N225   FTSE100     CAC40      GDAX       HSI
SP500   1.0000000 0.4666667 0.6666667 0.6666667 0.6666667 0.3333333
N225    0.4666667 1.0000000 0.3333333 0.3333333 0.4000000 0.4000000
FTSE100 0.6666667 0.3333333 1.0000000 0.7333333 0.6000000 0.4666667
CAC40   0.6666667 0.3333333 0.7333333 1.0000000 0.8000000 0.4666667
GDAX    0.6666667 0.4000000 0.6000000 0.8000000 1.0000000 0.4666667
HSI     0.3333333 0.4000000 0.4666667 0.4666667 0.4666667 1.0000000
SP500      N225   FTSE100     CAC40      GDAX       HSI
SP500   1.0000000 0.4666667 0.6666667 0.6666667 0.6666667 0.3333333
N225    0.4666667 1.0000000 0.3333333 0.3333333 0.4000000 0.4000000
FTSE100 0.6666667 0.3333333 1.0000000 0.7333333 0.6000000 0.4666667
CAC40   0.6666667 0.3333333 0.7333333 1.0000000 0.8000000 0.4666667
GDAX    0.6666667 0.4000000 0.6000000 0.8000000 1.0000000 0.4666667
HSI     0.3333333 0.4000000 0.4666667 0.4666667 0.4666667 1.0000000
```

FRAPO documentation built on May 2, 2019, 6:33 a.m.