ksmooth | R Documentation |
Implementation of simple Nadaraya-Watson nonparametric estimation of drift and diffusion coefficient, and plain kernel density estimation of the invariant density for a one-dimensional diffusion process.
ksdrift(x, bw, n = 512) ksdiff(x, bw, n = 512) ksdens(x, bw, n = 512)
x |
a |
bw |
bandwidth. |
n |
number of points in which to calculate the estimates. |
These functions return the nonparametric estimate of the drift or
diffusion coefficients for data x
using the Nadaraya-Watson estimator
for diffusion processes.
ksdens
returns the density estimates of the invariant density.
If not provided, the bandwidth bw
is calculated using Scott's rule (i.e.,
bw = len^(-1/5)*sd(x)
) where len=length(x)
is the number of observed points of the diffusion path.
val |
an invisible list of |
Stefano Maria Iacus
Ait-Sahalia, Y. (1996) Nonparametric pricing of interest rate derivative securities, Econometrica, 64, 527-560.
Bandi, F., Phillips, P. (2003) Fully nonparametric estimation of scalar diffusion models, Econometrica, 71, 241-283.
Florens-Zmirou, D. (1993) On estimating the diffusion coefficient from discrete observations, Journal of Applied Probability, 30, 790-804.
set.seed(123) theta <- c(6,2,1) X <- sde.sim(X0 = rsCIR(1, theta), model="CIR", theta=theta, N=1000,delta=0.1) b <- function(x) theta[1]-theta[2]*x sigma <- function(x) theta[3]*sqrt(x) minX <- min(X) maxX <- max(X) par(mfrow=c(3,1)) curve(b,minX,maxX) lines(ksdrift(X),lty=3) curve(sigma,minX, maxX) lines(ksdiff(X),lty=3) f <-function(x) dsCIR(x, theta) curve(f,minX,maxX) lines(ksdens(X),lty=3)
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