linear.mart.ef {sde}R Documentation

Linear martingale estimating function

Description

Apply linear martingale estimating function to find estimates of the parameters of a process solution of a stochastic differential equation.

Usage

linear.mart.ef(X, drift, sigma, a1, a2, guess, 
  lower, upper, c.mean, c.var) 

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.
a1, a2 weights or instruments
c.mean expressions for the conditional mean
c.var expressions for the conditional variance
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 linear.mart.ef minimizes a linear martinagale estimating function which is a particualr case of the polynomial martingale estimating functions (see references).

Value

x a vector of estimates

Note

This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.

Author(s)

Stefano Maria Iacus

References

Bibby, B., Soerensen, M. (1995) Martingale estimating functions for discretely observed diffusion processes, Bernoulli, 1, 17-39.

Examples

set.seed(123)
d <- expression(-1 * x)
s <- expression(1) 
x0 <- rnorm(1,sd=sqrt(1/2))
sde.sim(X0=x0,drift=d, sigma=s,N=1000,delta=0.1) -> X
 
d <- expression(-theta * x)
  
linear.mart.ef(X, d, s, a1=expression(-x), lower=0, upper=Inf,
  c.mean=expression(x*exp(-theta*0.1)), 
  c.var=expression((1-exp(-2*theta*0.1))/(2*theta)))

[Package sde version 1.9.14 Index]