Generate Conditionally Independent R-Many MA(4) Varying Time Series of the Same Length (Version 2)

generate_MA4_varyType2() generates R-many time series where the MA(4) that is used as the base coefficients for the variation is (-.3,-.6,-.3,.6). In this version of the data generation, only the first coefficient is changed, all other coefficients are left as is. This is based on the MA(4) used in Granados-Garcia et al. (2022) . This is the data generation that is used in Lee et al. (2025) .

Usage

generate_MA4_varyType2(n, R = 1, burn = 50, alpha = 0.05)

Arguments

n: A numeric vector that determines the length of the time series generated. Must contain R-many entries. Time series may be of different lengths.
R: An optional scalar indicating the number of conditionally independent time series to be generated. (default is 1).
burn: An optional scalar indicating the amount of burn-in to be used with stats::arima.sim(). (default is 50).
alpha: An optional scalar specifying the variation wanted from the first base coefficient. (default is 0.05).

Value

The function returns a list containing:

`ts_list`	returns an `R`-long list each containing an `(n[r]` \(\times\) `1)` matrix of the generated time series.
`true_theta`	returns a `(4` \(\times\) `R)` matrix of true generated MA(4) coefficients.

Details

The variation around the first base theta coefficient is generated by:

Sample 1 value from a \(N(0,1)\) to use as a "mean".
Calculate: basetheta[1] + alpha * mu_r * abs(basetheta[1]) where basetheta[1] is the original first MA(4) coefficient; mu_r is the 1 sampled values from the \(N(0,1)\); and alpha is the user-specified scalar that controls the variation around the first base coefficient.
Generate: A new time-series using the new theta value from step 2.
Repeat steps 1-3 R-many times.

Examples

R <- 20
## For time series of different lengths:
n <- c(rep(500, R / 2), rep(800, R / 2))
burn <- 50
alpha <- 0.05
ts <- generate_MA4_varyType2(n = n, R = R, burn = burn, alpha = alpha)$ts_list

# plot the time series generated:
# create an empty plot
plot(
  x = c(), y = c(),
  xlim = c(0, 800),
  ylim = range(ts),
  main = "Example",
  ylab = "",
  xlab = "time"
)
for (r in 1:10) {
  lines(ts[[r]][, 1], col = "blue")
}
for (r in 11:R) {
  lines(ts[[r]][, 1], col = "red")
}


## Returns an R-long list object each with a (500 x 1) matrix object,
## a (4 x 20) matrix of true MA(4) coefficients,
## a scalar returning the alpha provided,
## and a (4 x 20) matrix of the standard normal values generated for each R.