vineFit {vines}

Vine Inference

Description

Estimate a vine model from multivariate data in the unit hypercube. Data can be pseudo-observations constructed from empirical or parametric marginal cumulative distribution functions.

Usage

vineFit(type, data, method = "ml", ...)

Arguments

type

Type of vine. Supported values: "CVine" and "DVine".

data

Data matrix of pseudo-observations.

method

Inference method. Supported values: "ml" (Maximum Likelihood).

...

Additional arguments for the inference method.

Details

The "ml" (Maximum Likelihood) method starts with the sequential estimation procedure described in (Aas et al., 2009) and then executes a numerical maximization of the full log-likelihood of the vine. The sequential procedure is used to determine the family and the initial values of the parameters of each bivariate copula in the decomposition. Additional arguments for this method are:

selectCopula

Function provided by the user to select the copulas in the pair-copula construction. This function should return a copula object and expect the following arguments.

vine

Vine object being constructed.

j, i

Indexes of the copula under selection in the matrix of the copulas slot of the vine.

x, y

Bivariate sample.

The default value is function (vine, j, i, x, y) indepCopula() that assigns the independence copula to all the arcs of the vine.

trees

Maximum number of dependence trees of the vine. Independence copulas will be used in all the arcs of the following trees. The final number of dependence trees could be smaller because of the use of a truncation method. The default value is ncol(data) - 1.

truncMethod

Method used to automatically truncate the vine if enough dependence is captured in a given number of trees. Supported methods are "AIC" and "BIC". See (Brechmann, 2010; Brechmann et al., 2010) for information about these methods. The default value is "" that means no truncation.

optimMethod

optim method used in the optimization of the log-likelihood function. If "" is specified the optimization is disabled and the vine calculated using the sequential estimation procedure is returned. The default value is "Nelder-Mead".

optimControl

List of control parameters for optim. The default value is list().

Value

A vineFit object or a subclass with specific information about inference method used. The vine slot of this object contains the fitted Vine object.

References

Aas, K. and Czado, C. and Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44, 182–198.

Brechmann, E. C. (2010) Truncated and simplified regular vines and their applications. Diploma thesis. Technische Universitaet Muenchen.

Brechmann, E. C. and Czado, C. and Aas, K. (2010) Truncated regular vines in high dimensions with application to financial data. Norwegian Computing Center, NR. Note SAMBA/60/10.

See Also

CVine, DVine, vineFit, vineFitML.

Examples

data <- matrix(runif(5 * 100), ncol = 5, nrow = 100)
colnames(data) <- c("A", "B", "C", "D", "E")

selectCopula <- function (vine, j, i, x, y) {
    data <- cbind(x, y)
    fit <- fitCopula(normalCopula(), data, method = "itau")
    fit@copula
}
fit <- vineFit("DVine", data, method = "ml", 
               selectCopula = selectCopula, 
               optimMethod = "")

show(fit)
show(fit@vine)