# NOT RUN {
require(mgcv)
set.seed(0)
## Simulation parameters
# Sample size
n <- 1e3
# Copula families
familyset <- c(1:2, 301:304, 401:404)
# Define a 4-dimensional R-vine tree structure matrix
d <- 4
Matrix <- c(2, 3, 4, 1, 0, 3, 4, 1, 0, 0, 4, 1, 0, 0, 0, 1)
Matrix <- matrix(Matrix, d, d)
nnames <- paste("X", 1:d, sep = "")
## A function factory
eta0 <- 1
calib.surf <- list(
calib.quad <- function(t, Ti = 0, Tf = 1, b = 8) {
Tm <- (Tf - Ti) / 2
a <- -(b / 3) * (Tf^2 - 3 * Tf * Tm + 3 * Tm^2)
return(a + b * (t - Tm)^2)
},
calib.sin <- function(t, Ti = 0, Tf = 1, b = 1, f = 1) {
a <- b * (1 - 2 * Tf * pi / (f * Tf * pi +
cos(2 * f * pi * (Tf - Ti))
- cos(2 * f * pi * Ti)))
return((a + b) / 2 + (b - a) * sin(2 * f * pi * (t - Ti)) / 2)
},
calib.exp <- function(t, Ti = 0, Tf = 1, b = 2, s = Tf / 8) {
Tm <- (Tf - Ti) / 2
a <- (b * s * sqrt(2 * pi) / Tf) * (pnorm(0, Tm, s) - pnorm(Tf, Tm, s))
return(a + b * exp(-(t - Tm)^2 / (2 * s^2)))
}
)
## Create the model
# Define gam-vine model list
count <- 1
model <- vector(mode = "list", length = d * (d - 1) / 2)
sel <- seq(d, d^2 - d, by = d)
# First tree
for (i in 1:(d - 1)) {
# Select a copula family
family <- sample(familyset, 1)
model[[count]]$family <- family
# Use the canonical link and a randomly generated parameter
if (is.element(family, c(1, 2))) {
model[[count]]$par <- tanh(rnorm(1) / 2)
if (family == 2) {
model[[count]]$par2 <- 2 + exp(rnorm(1))
}
} else {
if (is.element(family, c(401:404))) {
rr <- rnorm(1)
model[[count]]$par <- sign(rr) * (1 + abs(rr))
} else {
model[[count]]$par <- rnorm(1)
}
model[[count]]$par2 <- 0
}
count <- count + 1
}
# A dummy dataset
data <- data.frame(u1 = runif(1e2), u2 = runif(1e2), matrix(runif(1e2 * d), 1e2, d))
# Trees 2 to (d-1)
for (j in 2:(d - 1)) {
for (i in 1:(d - j)) {
# Select a copula family
family <- sample(familyset, 1)
# Select the conditiong set and create a model formula
cond <- nnames[sort(Matrix[(d - j + 2):d, i])]
tmpform <- paste("~", paste(paste("s(", cond, ", k=10, bs='cr')",
sep = ""
), collapse = " + "))
l <- length(cond)
temp <- sample(3, l, replace = TRUE)
# Spline approximation of the true function
m <- 1e2
x <- matrix(seq(0, 1, length.out = m), nrow = m, ncol = 1)
if (l != 1) {
tmp.fct <- paste("function(x){eta0+",
paste(sapply(1:l, function(x)
paste("calib.surf[[", temp[x], "]](x[", x, "])",
sep = ""
)), collapse = "+"), "}",
sep = ""
)
tmp.fct <- eval(parse(text = tmp.fct))
x <- eval(parse(text = paste0("expand.grid(",
paste0(rep("x", l), collapse = ","), ")",
collapse = ""
)))
y <- apply(x, 1, tmp.fct)
} else {
tmp.fct <- function(x) eta0 + calib.surf[[temp]](x)
colnames(x) <- cond
y <- tmp.fct(x)
}
# Estimate the gam model
form <- as.formula(paste0("y", tmpform))
dd <- data.frame(y, x)
names(dd) <- c("y", cond)
b <- gam(form, data = dd)
# plot(x[,1],(y-fitted(b))/y)
# Create a dummy gamBiCop object
tmp <- gamBiCopFit(data = data, formula = form, family = 1, n.iters = 1)$res
# Update the copula family and the model coefficients
attr(tmp, "model")$coefficients <- coefficients(b)
attr(tmp, "model")$smooth <- b$smooth
attr(tmp, "family") <- family
if (family == 2) {
attr(tmp, "par2") <- 2 + exp(rnorm(1))
}
model[[count]] <- tmp
count <- count + 1
}
}
# Create the gamVineCopula object
GVC <- gamVine(Matrix = Matrix, model = model, names = nnames)
print(GVC)
# }
# NOT RUN {
## Simulate and fit the model
sim <- gamVineSimulate(n, GVC)
fitGVC <- gamVineSeqFit(sim, GVC, verbose = TRUE)
fitGVC2 <- gamVineCopSelect(sim, Matrix, verbose = TRUE)
## Plot the results
par(mfrow = c(3, 4))
plot(GVC, ylim = c(-2.5, 2.5))
plot(fitGVC, ylim = c(-2.5, 2.5))
plot(fitGVC2, ylim = c(-2.5, 2.5))
# }
# NOT RUN {
# }
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