simple.ef2 {sde} | R Documentation |
Apply 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.
simple.ef2(X, drift, sigma, h, h.x, h.xx, guess, lower, upper)
X |
a ts object containg a sample path of a sde. |
drift |
an expression for the drift coefficient. See details. |
sigma |
an expression for the diffusion coefficient. See details. |
h |
an expressions of `x' and the parameters to be estimated. See details. |
h.x |
an expressions of `x' containing the first derivative of h . See details. |
h.xx |
an expressions of `x' containing the second derivative of h . See details. |
guess |
initial value of the parameters. See details. |
lower |
lower bounds for the parameters. See details. |
upper |
upper bounds for the parameters. See 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
the application of the infinitesimal generator of the diffusion to the
functionn h
. This involves the drift and diffusion coefficient plus
the first two derivatives of h
. If not provided by the user, the derivatives
are caclulated by the function.
x |
a vector of estimates |
This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.
Stefano Maria Iacus
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.
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))