far (version 0.6-3)

simul.far.sde: FAR-SDE process simulation

Description

Simulation of a FAR process following an Stochastic Differential Equation

Usage

simul.far.sde(coef=c(0.4, 0.8), n=80, p=32, sigma=1)

Arguments

coef

Numerical vertor. It contains the two values of the coefficients ($a_1$ and $a_2$, see details for more informations).

n

Integer. The number of observations generated.

p

Integer. The number of discretization points.

sigma

Numeric. The standard deviation (see details for more informations).

Value

• A fdata object containing one variable ("var") which is a FAR(1) process of length n with p discretization points.

encoding

utf-8

Details

This function implements the simulation proposed by Besse and Cardot (1996) to simulate a FAR process following the Stochastic Differential Equation: $$dX^{(2)}+a_2.dX+a_1.X=\code{sigma}.dW$$ Where $dX^{(2)}$ and $dX$ stand respectively for the second and first derivate of the process X, and W is a brownian process. The coefficients $a_1$ and $a_2$ are the two first elements of coef. The simulation use a order one approximation inspired by the work of Milstein, as described in Besse and Cardot (1996).

References

Besse, P. and Cardot, H. (1996). Approximation spline de la prévision d'un processus fonctionnel autorégressif d'ordre 1. Revue Canadienne de Statistique/Canadian Journal of Statistics, 24, 467--487.

See Also

simul.far, simul.far.wiener, simul.farx, simul.wiener.

Examples

far1 <- simul.far.sde()
  summary(far1)
  print(far(far1,kn=2))
  par(mfrow=c(2,1))
  plot(far1,date=1)
  plot(select.fdata(far1,date=1:5),whole=TRUE,separator=TRUE)