Getting values from kernel density estimation in R

Question

I am trying to get density estimates for the log of stock prices in R. I know I can plot it using plot(density(x)). However, I actually want values for the function.

I'm trying to implement the kernel density estimation formula. Here's what I have so far:

a <- read.csv("boi_new.csv", header=FALSE)
S = a[,3] # takes column of increments in stock prices
dS=S[!is.na(S)] # omits first empty field

N = length(dS)                  # Sample size
rseed = 0                       # Random seed
x = rep(c(1:5),N/5)             # Inputted data

set.seed(rseed)   # Sets random seed for reproducibility

QL <- function(dS){
    h = density(dS)$bandwidth
    r = log(dS^2)
    f = 0*x
    for(i in 1:N){
        f[i] = 1/(N*h) * sum(dnorm((x-r[i])/h))
    }
    return(f)
}

QL(dS)

Any help would be much appreciated. Been at this for days!

Answer 1

You can pull the values directly from the density function:

x = rnorm(100)
d = density(x, from=-5, to = 5, n = 1000)
d$x
d$y

Alternatively, if you really want to write your own kernel density function, here's some code to get you started:

1. Set the points z and x range:

   z = c(-2, -1, 2)
   x = seq(-5, 5, 0.01)
   

2. Now we'll add the points to a graph

   plot(0, 0, xlim=c(-5, 5), ylim=c(-0.02, 0.8), 
        pch=NA, ylab="", xlab="z")
   for(i in 1:length(z)) {
      points(z[i], 0, pch="X", col=2)
   }
    abline(h=0)
   

3. Put Normal density's around each point:

   ## Now we combine the kernels,
   x_total = numeric(length(x))
   for(i in 1:length(x_total)) {
     for(j in 1:length(z)) {
       x_total[i] = x_total[i] + 
         dnorm(x[i], z[j], sd=1)
     }
   }
   

   and add the curves to the plot:

   lines(x, x_total, col=4, lty=2)
   

4. Finally, calculate the complete estimate:

   ## Just as a histogram is the sum of the boxes, 
   ## the kernel density estimate is just the sum of the bumps. 
   ## All that's left to do, is ensure that the estimate has the
   ## correct area, i.e. in this case we divide by $n=3$:
   
   plot(x, x_total/3, 
          xlim=c(-5, 5), ylim=c(-0.02, 0.8), 
          ylab="", xlab="z", type="l")
   abline(h=0)
   

   This corresponds to

   density(z, adjust=1, bw=1)
   

The plots above give: