Data generation

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 / 1/f)

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

Single model generation and plotting

model_single <- ar1(phi = 0.9, sigma2 = 1)
series_single <- generate(model_single, n = 500)
plot(series_single)

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

head(series_single$series)

## [1] 0.3362423 1.6150311 1.1883829 1.6127387 1.0371249 0.4571655

Generate and plot each base model

base_models <- list(
  wn(sigma2 = 1),
  ar1(phi = 0.7, sigma2 = 1),
  pl(kappa = 0.3, sigma2 = 2),
  matern(sigma2 = 1, lambda = 0.5, alpha = 1.0),
  rw(sigma2 = 0.2),
  flicker(sigma2 = 1)
)

par(mfrow = c(3, 2), mar = c(3, 4, 2, 1))
for (m in base_models) {
  s <- generate(m, n = 500)
  plot(s)
}

par(mfrow = c(1, 1))

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_comp <- wn(sigma2 = 1) + ar1(phi = 0.8, sigma2 = 0.5) + pl(kappa = 0.3, sigma2 = 2)
series_comp <- generate(model_comp, n = 500)
plot(series_comp)

More composite model examples

comp_models <- list(
  wn(sigma2 = 2) + rw(sigma2 = 0.1),
  wn(sigma2 = 1) + ar1(phi = 0.95, sigma2 = 0.3) + flicker(sigma2 = 0.5),
  pl(kappa = 0.4, sigma2 = 1) + matern(sigma2 = 0.8, lambda = 0.6, alpha = 1.2)
)

par(mfrow = c(3, 1), mar = c(3, 4, 2, 1))
for (m in comp_models) {
  s <- generate(m, n = 500)
  plot(s)
}

par(mfrow = c(1, 1))

The composite output is a generated_composite_model_time_series with:

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

names(series_comp)

## [1] "series"     "components" "n"          "model"      "parameters"

Combining and plotting

The plot() method for a composite model stacks each component vertically and adds the sum at the top. For single models, plot() draws the time series with the model name in the title.