drw.sim: Simulating Univariate and Multivariate Damped Random Walk...

In Rdrw: Univariate and Multivariate Damped Random Walk Processes

Simulating Univariate and Multivariate Damped Random Walk Processes

Description

The function drw.sim simulates one or more time series from univariate or multivariate damped random walk processes.

Usage

drw.sim(time, n.datasets, measure.error.SD, mu, sigma, tau, rho)

Arguments

time	A vector of observation times. Let n denote the length of this vector.
n.datasets	A positive integer giving the number of time series to be simulated. In simulation, there is no upper limit on the number of time series. Let k denote this number.
measure.error.SD	Optional measurement error standard deviations. If one time series is simulated, this is a vector of length n. If more than one time series is simulated, this is an n by k matrix of measurement error standard deviations. If this information is unavailable, it is automatically set to zero.
mu	A vector of length k containing the long-term mean parameter or parameters.
sigma	A vector of length k containing the short-term variability parameter or parameters, expressed as standard deviations.
tau	A vector of length k containing the timescale parameter or parameters.
rho	Required when more than one time series is simulated, k > 1. This is a vector of length k(k - 1) / 2 containing the cross-correlation parameters. For example, if k = 3, this vector contains rho_12, rho_13, and rho_23. If k = 5, this vector contains rho_12, rho_13, rho_14, rho_15, rho_23, rho_24, rho_25, rho_34, rho_35, and rho_45.

Details

Given observation times and model parameter values mu, sigma, tau, and optionally rho, this function simulates k time series, optionally including known measurement error standard deviations.

Value

The output of drw.sim is a list containing:

x

An n by k matrix of simulated time series. Each column corresponds to one simulated time series.

Author(s)

Zhirui Hu and Hyungsuk Tak

References

Zhirui Hu and Hyungsuk Tak (2020), "Modeling Stochastic Variability in Multi-Band Time Series Data," doi:10.3847/1538-3881/abc1e2.

Examples

########## Simulating a multivariate damped random walk process

n <- 100
k <- 5
obs.time <- cumsum(rgamma(n, shape = 3, rate = 1))

tau <- 100 + 20 * (1:5)
sigma <- 0.01 * (1:5)
mu <- 17 + 0.5 * (1:5)

rho.m <- matrix(0, k, k)
for (i in 1:k) {
  for (j in 1:k) {
    rho.m[i, j] <- 1.1^(-abs(i - j))
  }
}

rho <- rho.m[upper.tri(rho.m)]

measure.error.band <- c(0.010, 0.014, 0.018, 0.022, 0.026)
measure.error <- NULL
for (i in 1:k) {
  measure.error <- cbind(measure.error, rnorm(n, measure.error.band[i], 0.002))
}

x <- drw.sim(time = obs.time, n.datasets = 5, measure.error.SD = measure.error,
             mu = mu, sigma = sigma, tau = tau, rho = rho)

plot(obs.time, x[, 1], xlim = c(min(obs.time), max(obs.time)), ylim = c(17, 20),
     xlab = "time", ylab = "observation")
points(obs.time, x[, 2], col = 2, pch = 2)
points(obs.time, x[, 3], col = 3, pch = 3)
points(obs.time, x[, 4], col = 4, pch = 4)
points(obs.time, x[, 5], col = 5, pch = 5)

########## Simulating a univariate damped random walk process

x <- drw.sim(time = obs.time, n.datasets = 1, measure.error.SD = measure.error[, 1],
             mu = mu[1], sigma = sigma[1], tau = tau[1])
plot(obs.time, x)

Rdrw documentation built on Aug. 20, 2026, 5:09 p.m.