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, ie 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: