simple.ef2 {sde} | R Documentation |
Simple estimating function based on the infinitesimal generator a the diffusion process
Description
Apply a simple estimating function based on the infinitesimal generator of a diffusion to find estimates of the parameters of a process solution of that particular stochastic differential equation.
Usage
simple.ef2(X, drift, sigma, h, h.x, h.xx, guess, lower,
upper)
Arguments
X |
a |
drift |
an expression for the drift coefficient; see details. |
sigma |
an expression for the diffusion coefficient; see details. |
h |
an expression of |
h.x |
an expression of |
h.xx |
an expression of |
guess |
initial value of the parameters; see details. |
lower |
lower bounds for the parameters; see details. |
upper |
upper bounds for the parameters; see details. |
Details
The function simple.ef2
minimizes the simple estimating function
of the form sum_i f_i(x;theta) = 0
, where f
is the result of
applying the infinitesimal generator of the diffusion to the
function h
. This involves the drift and diffusion coefficients plus
the first two derivatives of h
. If not provided by the user, the derivatives
are calculated by the function.
Value
x |
a vector of estimates |
Author(s)
Stefano Maria Iacus
References
Kessler, M. (1997) Estimation of an ergodic diffusion from discrete observations, Scand. J. Statist., 24, 211-229.
Kessler, M. (2000) Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process, Scand. J. Statist., 27, 65-82.
Examples
set.seed(123)
d <- expression(10 - x)
s <- expression(sqrt(x))
x0 <- 10
sde.sim(X0=x0,drift=d, sigma=s,N=1500,delta=0.1) -> X
# rather difficult problem unless a good initial guess is given
d <- expression(alpha + theta*x)
s <- expression(x^gamma)
h <- list(expression(x), expression(x^2), expression(x^2))
simple.ef2(X, d, s, h, lower=c(0,-Inf,0), upper=c(Inf,0,1))