CDVineCondSim: Simulation from a conditional C- or D-vine

Description

Simulates from a d-dimensional conditional C- or D-vine of the variables (Y,X), given the fixed conditioning variables X. The algorithm works for vines satysfying the requirements discussed in Bevacqua et al. (2017). The algorthm implemented here is a modified version of those form Aas et al. (2009) and is shown in Bevacqua et al. (2017).

Usage

CDVineCondSim(RVM, Condition, N)

Arguments

RVM

An RVineMatrix object containing the information of the d-dimensional C- or D-Vine model (for further details about RVineMatrix objects see the documentation file of the VineCopula package). If the full copula is 2-dimensional, RVM can be an RVineMatrix object or a data.frame (or list) object where $family, $par and $par2 are specified.

Condition

A N x Nx matrix of the Nx conditioning variables. For D-vine: data corresponding to the conditioning variable whose index is in RVM$Matrix[i,i], are in i-th column of Condition. For C-vine: data corresponding to the conditioning variable whose index is in RVM$Matrix[i,i], are in [(d+1)-i]-th column of Condition. See examples.

Number of data to be simulated. By default N is taken from Condition, which is a N x Nx matrix. It is necessary to specify N only when Condition is not given.

Value

A N x d matrix of the simulated variables from the given C- or D-vine copula model. In the first columns there are the simulated conditioned variables, and in the last columns the conditioning variables Condition. For more details about the exact order of the variables in the columns see the examples. The function is built to work easily in combination with CDVineCondFit.

References

Bevacqua, E., Maraun, D., Hobaek Haff, I., Widmann, M., and Vrac, M.: Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy), Hydrol. Earth Syst. Sci., 21, 2701-2723, https://doi.org/10.5194/hess-21-2701-2017, 2017. [link] [link]

Aas, K., Czado, C., Frigessi, A. and Bakken, H.: Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics, 44(2), 182-198, <doi:10.1016/j.insmatheco.2007.02.001>, 2009. [link]

Ulf Schepsmeier, Jakob Stoeber, Eike Christian Brechmann, Benedikt Graeler, Thomas Nagler and Tobias Erhardt (2017). VineCopula: Statistical Inference of Vine Copulas. R package version 2.1.1. [link]

Examples

Run this code

# NOT RUN {
# Example 1: conditional sampling from a C-Vine

# Read data
data(dataset) 
data <- dataset$data[1:400,1:4]

# Define the variables Y and X. X are the conditioning variables, 
# which have to be positioned in the last columns of the data.frame
colnames(data) <- c("Y1","Y2","X3","X4")

# }
# NOT RUN {
# Select a vine and fit the copula families, specifying that there are 2 conditioning variables
RVM <- CDVineCondFit(data,Nx=2,type="CVine")

# Set the values of the conditioning variables as those used for the calibration. 
# Order them with respect to RVM$Matrix, considering that is a C-Vine
d=dim(RVM$Matrix)[1]
cond1 <- data[,RVM$Matrix[(d+1)-1,(d+1)-1]]
cond2 <- data[,RVM$Matrix[(d+1)-2,(d+1)-2]]
condition <- cbind(cond1,cond2)

# Simulate the variables
Sim <- CDVineCondSim(RVM,condition)

# Plot the simulated variables over the observed
Sim <- data.frame(Sim)
overplot(Sim,data)



# Example 2: conditional sampling from a D-Vine

# Read data
data(dataset) 
data <- dataset$data[1:100,1:4]

# Define the variables Y and X. X are the conditioning variables, 
# which have to be positioned in the last columns of the data.frame
colnames(data) <- c("Y1","Y2","X3","X4")

# Select a vine and fit the copula families, specifying that there are 2 conditioning variables
RVM <- CDVineCondFit(data,Nx=2,type="DVine")
summary(RVM) #It is a D-Vine.

# Set the values of the conditioning variables as those used for the calibration. 
# Order them with respect to RVM$Matrix, considering that is a D-Vine.
cond1 <- data[,RVM$Matrix[1,1]]
cond2 <- data[,RVM$Matrix[2,2]]
condition <- cbind(cond1,cond2)

# Simulate the variables
Sim <- CDVineCondSim(RVM,condition)

# Plot the simulated variables over the observed
Sim <- data.frame(Sim)
overplot(Sim,data)



# Example 3

# Read data
data(dataset) 
data <- dataset$data[1:100,1:2]
colnames(data) <- c("Y1","X2")

# Fit copula
require(VineCopula)
BiCop <- BiCopSelect(data$Y1,data$X2)
BiCop

# Fix conditioning variable to low values and simulate
condition <- data$X2/10
Sim <- CDVineCondSim(BiCop,condition)

# Plot the simulated variables over the observed
Sim <- data.frame(Sim)
overplot(Sim,data)
# }
# NOT RUN {
# }