linear.mart.ef {sde} | R Documentation |
Apply linear martingale estimating function to find estimates of the parameters of a process solution of a stochastic differential equation.
linear.mart.ef(X, drift, sigma, a1, a2, guess, lower, upper, c.mean, c.var)
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. |
The function linear.mart.ef
minimizes a linear martinagale
estimating function which is a particualr case of the polynomial
martingale estimating functions (see references).
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
Bibby, B., Soerensen, M. (1995) Martingale estimating functions for discretely observed diffusion processes, Bernoulli, 1, 17-39.
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)))