gofKendallKS tests a given dataset for a copula based on Kendall's process with the Kolmogorov-Smirnof test statistic. The margins can be estimated by a bunch of distributions and the time which is necessary for the estimation can be given. The possible copulae are "normal", "t", "gumbel", "clayton" and "frank". See for reference Genest et al. (2009). The parameter estimation is performed with pseudo maximum likelihood method. In case the estimation fails, inversion of Kendall's tau is used. The approximate p-values are computed with a parametric bootstrap, which computation can be accelerated by enabling in-build parallel computation.
gofKendallKS(copula, x, param = 0.5, param.est = T, df = 4, df.est = T, margins = "ranks", dispstr = "ex", M = 100, execute.times.comp = T, processes = 1)"normal", "t", "clayton", "gumbel" and "frank".
TRUE or FALSE. TRUE means that param will be estimated.
"t"-copula.
df shall be estimated. Has to be either FALSE or TRUE, whereTRUE means that it will be estimated.
"ranks", which is the standard approach to convert data in such a case. Alternatively can the following distributions be specified: "beta", "cauchy", Chi-squared ("chisq"), "f", "gamma", Log normal ("lnorm"), Normal ("norm"), "t", "weibull", Exponential ("exp").
copula.
M is at least 100.
class gofCOP with the components
gofCOP with the componentsBecause $H0^'$ consists of more distributions than the $H0$ is the test not necessarily consistent.
The approximate p-value is computed by the formula
$$\sum_{b=1}^M \mathbf{I}(|T_b| \geq |T|) / M,$$
For small values of M, initializing the parallization via processes does not make sense. The registration of the parallel processes increases the computation time. Please consider to enable parallelization just for high values of M.
data(IndexReturns)
gofKendallKS("normal", IndexReturns[c(1:100),c(1:2)], M = 10)
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