Data generation

In gmwmx2: Estimate Functional and Stochastic Parameters of Linear Models with Correlated Residuals and Missing Data

knitr::opts_chunk$set(
  fig.width = 10,
  fig.height = 6,
  fig.align = "center"
)

This vignette shows how to build stochastic models, combine them with +, generate data, and plot the results.

library(gmwmx2)
set.seed(123)

Available models

You can build a single stochastic process with any of the following model constructors:

• wn() (white noise)
• ar1() (AR(1))
• pl() (power-law)
• matern() (Matérn)
• rw() (random walk)
• flicker() (flicker)

Each constructor returns a time_series_model object that can be plotted or combined with others using +.

Stochastic models

White noise

model_wn <- wn(sigma2 = 1)
series_wn <- generate(model_wn, n = 500)
plot(series_wn)

The generated object is a generated_time_series with a numeric series in $series:

head(series_wn$series)

AR(1)

model_ar1 <- ar1(phi = 0.8, sigma2 = 1)
series_ar1 <- generate(model_ar1, n = 500)
plot(series_ar1)

Power-law

model_pl <- pl(kappa = 0.3, sigma2 = 1)
series_pl <- generate(model_pl, n = 500)
plot(series_pl)

Matérn

model_matern <- matern(sigma2 = 1, lambda = 1, alpha=1)
series_matern <- generate(model_matern, n = 500)
plot(series_matern)

Random walk

model_rw <- rw(sigma2 = 0.1)
series_rw <- generate(model_rw, n = 500)
plot(series_rw)

Flicker

model_fl <- flicker(sigma2 = 1)
series_fl <- generate(model_fl, n = 500)
plot(series_fl)

Reproducible generation

You can set a random seed before calling generate(), or pass a seed directly to generate(), to make the output deterministic. Using the same seed and model parameters produces the exact same time series.

model_wn <- wn(sigma2 = 1)

set.seed(1234)
series_a <- generate(model_wn, n = 100)

series_b <- generate(model_wn, n = 100, seed = 1234)
series_c <- generate(model_wn, n = 100, seed = 4321)

all.equal(series_a$series, series_b$series)
all.equal(series_a$series, series_c$series)

Composite models (sum of processes)

Use + to build a composite model from multiple stochastic processes. The result is a sum_model that can be passed to generate().

model_wn_ar1 <- wn(sigma2 = 1) + ar1(phi = 0.8, sigma2 = 0.5)
class(model_wn_ar1)
series_wn_ar1 <- generate(model_wn_ar1, n = 500)
plot(series_wn_ar1)

The composite output is a generated_composite_model_time_series with:

• series (the total sum)
• components (a list of each component series)
• n (length of the series)
• model (names of each component)
• parameters (parameters of each component)

names(series_wn_ar1)

gmwmx2 documentation built on June 10, 2026, 5:06 p.m.