r

Question

我正在使用R软件包costrOptim.nl。

我需要最小化具有以下约束的函数：

Alpha < sqrt(2*omega) and omega > 0

在我的代码中表示为：

theta[3] < sqrt(2*theta[1]) and theta[1] > 0 

我将这些条件写为：

Image

但是当我打电话给optimizer并运行它时。

我遇到以下问题：

1: In sqrt(2 * theta[1]) : NaNs produced

为什么？我设置了适当的条件吗？

Answer 1

This is my whole code. 

data <- read.delim(file = file, header = FALSE)
ind <- seq(from = 1, to = NROW(data), by = 1)
data <- data.frame(ind = ind, Ret = data$V1, Ret2 = data$V1^2)

colnames(data)[1] <- "Ind"
colnames(data)[2] <- "Ret"
colnames(data)[3] <- "Ret2"
T <- length(data$Ret)

m <- arima(x = data$Ret2, order = c(3,0,0), include.mean = TRUE, method = c("ML"))

b_not <- m$coef

omega <- 0.1
alpha <- 0.005
beta <-  0.9

theta <- c(omega,beta,alpha) # "some" value of theta

s0 <- theta[1]/(1-theta[2])


theta[3] < sqrt(2*theta[1]) # check whether the Feller condition is verified 

N <- 30000 
reps <- 1
rho <- -0.8
n <- 100

heston.II <- function(theta){
set.seed(5)
u <- rnorm(n = N*reps,mean = 0, sd = 1)
u1 <- rnorm(n = N*reps,mean = 0, sd = 1)
u2 <- rho*u + sqrt((1-rho^2))*u1

sigma <- matrix(0, nrow = N*reps, ncol = 1)
ret.int <- matrix(0, nrow = N*reps, ncol = 1)
sigma[1,1] <- s0

for (i in 2:(N*reps)) {
sigma[i,1] <- theta[1] + theta[2]*sigma[i-1,1] + theta[3]*sqrt(sigma[i-1,1])*u1[i]
 # if(sigma[i,1] < 0.00000001){ sigma[i,1] =  s0}
}

for (i in 1:(N*reps)) {
ret.int[i,1] <- sqrt(sigma[i,1])*u2[i]
}


ret <- matrix(0, nrow = N*reps/n, ncol = 1)
ret[1,1] <- sum(ret.int[1:n],1)

for (i in 2:((N*reps)/n)) {
ret[i,] <- sum(ret.int[(n*i):(n*(i+1))])
ret[((N*reps)/n),] <- sum(ret.int[(n*(i-1)):(n*i)])
}

ret2 <- ret^2 

model <- arima(x = ret2, order = c(3,0,0), include.mean = TRUE)

beta_hat <- model$coef
m1 <- beta_hat[1] - b_not[1]
m2 <- beta_hat[2] - b_not[2]
m3 <- beta_hat[3] - b_not[3]
m4 <- beta_hat[4] - b_not[4]

D <- cbind(m1,m2,m3,m4)

DD <- (D)%*%t(D)/1000
DD <- as.numeric(DD)
return(DD)

}

heston.sim <- heston.II(theta)

hin <- function(theta){
h <- rep(NA, 2)
h[1] <- theta[1] 
h[2] <- sqrt(2*theta[1]) - theta[3]
return(h)
}

hin(theta = theta)

.opt <- constrOptim.nl(par = theta, fn = heston.II, hin = hin)
.opt