linear.mart.ef: Linear martingale estimating function

In sde: Simulation and Inference for Stochastic Differential Equations

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)))

sde documentation built on Sept. 9, 2022, 3:07 p.m.