simul.far.sde | R Documentation |
Simulation of a FAR process following an Stochastic Differential Equation
simul.far.sde(coef=c(0.4, 0.8), n=80, p=32, sigma=1)
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). |
This function implements the simulation proposed by Besse and Cardot (1996) to simulate a FAR process following the Stochastic Differential Equation:
d^2(X)+a(2).d(X)+a(1).X=\code{sigma}.d(W)
Where d^2(X) and d(X) 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).
A fdata
object containing one variable ("var") which is a
FAR(1) process of length n
with p
discretization
points.
J. Damon
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.
simul.far
, simul.far.wiener
,
simul.farx
, simul.wiener
.
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)
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