simple.ef2 {sde}R Documentation

Simple estimating function based on infinitesimal generator

Description

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.

Usage

simple.ef2(X, drift, sigma, h, h.x, h.xx, guess, lower, upper) 

Arguments

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.

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.

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))

[Package sde version 1.9.33 Index]