randOU {timedeppar}

Draw from an Ornstein-Uhlenbeck process

Description

This function draws a realization of an Ornstein-Uhlenbeck process with a random start value (drawn from the marginal distribution), conditional of the start value, or conditional on both start and end values. The function includes the option of obtaining a lognormal marginal by exponential tranformation.

Usage

randOU(
  mean = 0,
  sd = 1,
  gamma = 1,
  t = 0:1000/1000,
  yini = NA,
  yend = NA,
  log = FALSE
)

Arguments

mean

asymptotic mean of the process.

sd

asymptotic standard deviation of the process

gamma

rate coefficient for return to the mean

t

vector of time points at which the process should be sampled (note: the value at t[1] will be the starting value yini, the value at t[length(t)] the end value yend if these are specified)

yini

start value of the process (NA indicates random with asymptotic mean and sd)

yend

end value of the process (NA indicates no conditioning at the end)

log

indicator whether the log of the variable should be an Ornstein-Uhlenbeck process (log=TRUE) rather than the variable itself (mean and sd are interpreted in original units also for log=TRUE)

Value

a data frame with t and y columns for time and for the realization of the Ornstein-Uhlenbeck process

Examples

plot(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000),type="l",ylim=2.5*c(-1,1))
abline(h=0)
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000),col="red")
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000),col="blue")
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000),col="green")

plot(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000,yini=0,yend=0),type="l",ylim=2.5*c(-1,1))
abline(h=0)
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000,yini=0,yend=0),col="red")
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000,yini=0,yend=0),col="blue")
lines(randOU(mean=0,sd=1,gamma=1,t=0:1000/1000,yini=0,yend=0),col="green")