# vineFit: Vine Inference In vines: Multivariate Dependence Modeling with Vines

## 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

 `1` ```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.

`CVine`, `DVine`, `vineFit`, `vineFitML`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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) ```

### Example output

```Loading required package: copula
Vine Inference

Method: ml
Vine type: D-vine
Dimension: 5
Observations: 100
Optimization method:
Convergence code: 0
Vine

Type: D-vine
Dimension: 5
Dependency trees: 4

A,B: <deprecated slot> (rho.1 = 0.100740584026723)
B,C: <deprecated slot> (rho.1 = 0.103897253837734)
C,D: <deprecated slot> (rho.1 = 0.0520190559151636)
D,E: <deprecated slot> (rho.1 = 0.0260183360543773)

A,C|B: <deprecated slot> (rho.1 = 0.0374364957639043)
B,D|C: <deprecated slot> (rho.1 = 0.0298248401712931)
C,E|D: <deprecated slot> (rho.1 = -0.0228459587429497)

A,D|B,C: <deprecated slot> (rho.1 = -0.167394490441731)
B,E|C,D: <deprecated slot> (rho.1 = -0.219072212989425)

A,E|B,C,D: <deprecated slot> (rho.1 = 0.112099619611967)
```

vines documentation built on May 29, 2017, 6:53 p.m.