Simulate several random processes.

Simulate Functional Data from different processes: Ornstein Uhlenbeck, Brownian, Fractional Brownian, Gaussian or Exponential variogram.

Usage

rproc2fdata(
  n,
  t = NULL,
  mu = rep(0, length(t)),
  sigma = 1,
  par.list = list(scale = 1, theta = 0.2 * diff(rtt), H = 0.5),
  norm = FALSE,
  verbose = FALSE,
  ...
)

Arguments

n

Number of functional curves to be generated.

t

Discretization points.

mu

vector which specifies the trend values at the discretization points, by default mu=\(\mu(t)=0\). If mu is a fdata class object, t\(=\)argvals(mu).

sigma

A positive-definite symmetric matrix, \(\Sigma_{s,t}\), specifying the covariance matrix among grid points. If sigma is a scalar, creates a random Gaussian process with \(\Sigma_{s,t}=\)sigmaI (by default sigma=1).
If sigma is a vector, creates a random Gaussian process with \(\Sigma_{s,t}=\)diag(sigma).
If sigma is a character: create a random process using the covariance matrix \(\Sigma_{s,t}\) indicated in the argument,

• "OU" or "OrnsteinUhlenbeck", creates a random Ornstein Uhlenbeck process with \(\Sigma_{s,t}=\frac{\sigma^2}{2\theta}e^{-\theta\left(s+t\right)} \left(e^{2\theta\left(s+t\right)}-1\right)\), by default \(\theta=1/(3range(t))\), \(\sigma^2={1}\).

• "brownian" or "wiener", creates a random Wiener process with \(\Sigma_{s,t}=\sigma^2 min(s,t)\), by default \(\sigma^2=1\).

• "fbrownian", creates a random fractional brownian process with \(\Sigma_{s,t}=\sigma^{2H}/2{|s|^{2H}+|t|^{2H}-|s-t|^{2H}}\), by default \(\sigma^2=1\) and \(H=0.5\) (brownian process).

• "vexponential", creates a random gaussian process with exponential variogram \(\Sigma_{s,t}=\sigma^2 e^{\left(-\frac{\left|s-t\right|}{\theta}\right)}\), by default \(\theta={0.2 range(t)}\), \(\sigma^2={1}\).

par.list

List of parameter to process, by default "scale" \(\sigma^2=1\),
"theta" \(\theta=0.2 range(t)\) and "H"=0.5.

norm

If TRUE the norm of random projection is 1. Default is FALSE

verbose

If TRUE, information about procedure is printed. Default is FALSE.

...

Further arguments passed to or from other methods.

Value

Return the functional random processes as a fdata class object.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
par(mfrow=c(3,2))
lent<-30
tt<-seq(0,1,len=lent)
mu<-fdata(rep(0,lent),tt)
plot(rproc2fdata(200,t=tt,sigma="OU",par.list=list("scale"=1)))
plot(rproc2fdata(200,mu=mu,sigma="OU",par.list=list("scale"=1)))
plot(rproc2fdata(200,t=tt,sigma="vexponential"))
plot(rproc2fdata(200,t=tt,sigma=1:lent))
plot(rproc2fdata(200,t=tt,sigma="brownian"))
plot(rproc2fdata(200,t=tt,sigma="wiener"))
#plot(rproc2fdata(200,seq(0,1,len=30),sigma="oo")) # this is an error 
} # }