kcop: The Bivariate K-Copula
In mlkremer/kcopula: The Bivariate K-Copula

Description Usage Arguments Value Author(s) References Examples

Density and distribution function of the bivariate K-copula by Wollschläger and Schäfer (2016).

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pkcopula(u, v, c, N, output = "vector", method = "interpolate")

dkcopula(u, v, c, N, output = "vector")

`u, v`	Numeric vectors with values in [0, 1].
`c`	Numeric; Pearson correlation coefficient in [-1, 1].
`N`	Numeric; inverse fluctuation strength of correlations around their average `c`, N>0. The larger `N` the smaller the fluctuations around `c`, and vice versa.
`output`	Character; output as "vector" (default) for single values of the K-copula, or "matrix" for the full K-copula.
`method`	Character; method to be used for `pkcopula(..., output = "vector")`. If `method = "interpolate"` (default), values are computed by interpolating the bivariate K-copula distribution function (computationally faster); returns `NA`, if `u, v` are out of range (here: outside of [.025, .975]). If `method = "integrate"`, values are computed by integrating the bivariate K-copula density (computationally slower).

dkcopula gives the density (PDF), pkcopula gives the distribution function (CDF) of the bivariate K-copula.

Marcel Kremer, marcel.kremer@uni-due.de

Wollschläger, M. and Schäfer, R. (2016). Impact of nonstationarity on estimating and modeling empirical copulas of daily stock returns. Journal of Risk, 19(1):1–23. https://doi.org/10.21314/JOR.2016.342. SSRN version: https://ssrn.com/abstract=3533903.

Chetalova, D., Wollschläger, M., and Schäfer, R. (2015). Dependence structure of market states. Journal of Statistical Mechanics: Theory and Experiment, 2015(8):P08012. https://doi.org/10.1088/1742-5468/2015/08/P08012. SSRN version: https://ssrn.com/abstract=3533951.

## Parameters
u <- seq(.05, .95, .05)
v <- u
rho <- .2
N <- 4

## K-copula PDF
dkcopula(.5, .5, rho, N)


## Plot full K-copula PDF
kcopula_pdf <- dkcopula(u, v, rho, N, output = "matrix")
persp(u, v, kcopula_pdf)

## K-copula CDF
pkcopula(.5, .5, rho, N)

## Plot full K-copula CDF
kcopula_cdf <- pkcopula(u, v, rho, N, output = "matrix")
persp(u, v, kcopula_cdf)