# R/inferH.R In HKprocess: Hurst-Kolmogorov Process

#### Documented in inferH

```inferH <- function(data,n,add = 0.001,minu = 0.001,maxu = 0.999) {
# Set natural logarithm of eq. 10 in Tyralis and Koutsoyiannis (2014)
logphxfunction <- function(H,x) {
size = length(x)
maxlag <- size - 1
a1 <- ltza(acfHKp(H,maxlag),x)

-0.5*a1[4]-0.5*(size-1)*log(a1[3]*a1[1]-(a1[2])^2)+(0.5*size-1)*
log(a1[3])
}

# Set a function to find the maximum of logphxfunction
optimprice <- function(x) {
f <- function(H) {logphxfunction(H,x = x)}

as.vector(unlist(optimize(f = f,interval = c(0.00001,0.99999),
maximum = TRUE)[2]))
}
logM <- optimprice(data) # Maximum value of logphxfunction
# An Accept-Reject algorithm to simulate from H
accrej <- function(x,logM,add,minu = minu,maxu = maxu) {
dist = 1/(maxu - minu)
f <- function(H) {logphxfunction(H,x = x)}
logM1 <- logM - log(dist) + add
u <- runif(1,min=0,max=1)
logu <- log(u) + logM1
y <- runif(1,min = minu,max = maxu)
while (logu > f(y) - log(dist))
{u <- runif(1,min = 0,max = 1)
logu <- log(u) + logM1
y <- runif(1,min = minu,max = maxu)
}
y
}
y <- c()
for (i in 1:n) {
y[i] <- accrej(x = data,logM,add,minu = minu,maxu = maxu)
}
return(y)
}
```

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HKprocess documentation built on May 29, 2017, 9:20 p.m.