R: Nonparametric invariant density, drift, and diffusion...
ksmooth
R Documentation
Nonparametric invariant density, drift, and diffusion coefficient estimation
Description
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.
Usage
ksdrift(x, bw, n = 512)
ksdiff(x, bw, n = 512)
ksdens(x, bw, n = 512)
Arguments
x
a ts object.
bw
bandwidth.
n
number of points in which to calculate the estimates.
Details
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.
Value
val
an invisible list of x and y coordinates
and an object of class density in the case of invariant
density estimation
Author(s)
Stefano Maria Iacus
References
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.