Simulate from a Multi-Seasonal ARIMA Model (Direct Interface)

Simulates a time series from a multi-seasonal ARIMA model with specified parameters. This function provides a direct interface for simulation without requiring a fitted model object.

Usage

msarima.sim(
  nsim,
  order = c(0, 0, 0),
  seasonal = list(),
  seasonal.period = NULL,
  ar = NULL,
  ma = NULL,
  sigma2 = 1,
  burn = NULL,
  intercept = 0
)

Arguments

nsim

Length of the simulated series (required).

order

A numeric vector of length 3 specifying the non-seasonal part of the ARIMA model: the AR order (p), the degree of differencing (d), and the MA order (q). Default is c(0, 0, 0).

seasonal

A list of numeric vectors, each of length 3, specifying the seasonal components. Each vector gives the seasonal AR order (P), the seasonal differencing order (D), and the seasonal MA order (Q) of one component. Use list() for a model without seasonal components. Default is list().

seasonal.period

A numeric vector of seasonal periods, one for each element of seasonal. Periods can be given in any order but must be distinct. Default is NULL.

ar

Numeric vector of AR coefficients, non-seasonal first and then one block per seasonal component. Its length must match the total AR order implied by order and seasonal. Default is NULL.

ma

Numeric vector of MA coefficients, ordered as ar. Its length must match the total MA order implied by order and seasonal. Default is NULL.

sigma2

Innovation variance. Default is 1.

burn

Number of burn-in observations to discard. If NULL, it is set to max(100, 2 * kk), where kk is the largest lag in the model. Default is NULL.

intercept

Constant term of the model equation, that is \(\mu\) in \(y_t = \mu + \sum \phi_i y_{t-i} + \sum \theta_j e_{t-j} + e_t\). This is the intercept, not the mean of the process: for a stationary model the mean is intercept / prod(1 - ar). Default is 0.

Value

A time series object of length nsim: ts with one seasonal period, msts with several.

See also

msarima, simulate.msarima

Examples

# Simulate data
set.seed(123)
y <- msarima.sim(nsim = 200,
                 order = c(1, 0, 0),
                 seasonal = list(c(1, 0, 0), c(0, 0, 1)),
                 seasonal.period = c(4, 11),
                 ar = c(0.5, 0.5), ma = 0.3, sigma2 = 1)