linear.mart.ef {sde}

Linear martingale estimating function

Description

Apply a 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 containing a sample path of an 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 martingale estimating function that is a particular case of the polynomial martingale estimating functions.

Value

x

a vector of estimates

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)))