When simulating realizations from ARIMA processes, you need presample responses and presample innovations to initialize the conditional mean model. The number of presample responses you need to initialize a simulation are stored in the
arima model property
P. The number of presample innovations you need to initialize a simulation are stored in the property
Q. You can specify your own presample data or let
simulate generate presample data.
If you let
simulate generate default presample data, then:
For stationary processes,
simulate sets presample responses to the unconditional mean of the process.
For nonstationary processes,
simulate sets presample responses to 0.
Presample innovations are set to 0.
If you specify a matrix of exogenous covariates, then
simulate sets the presample responses to 0.