You can use Monte Carlo simulation to forecast an error process over a future time horizon. This is an alternative to minimum mean square error (MMSE) forecasting, which provides an analytical forecast solution. You can calculate MMSE forecasts using
To forecast a process using Monte Carlo simulation:
Fit a model to your observed series using
estimate, or fully specify a
Infer residuals (estimated innovations) and unconditional disturbances from the model using
infer and the data. The inferred series are presample observations.
Generate many sample paths over the forecast horizon using
simulate and the presample observations.
An advantage of Monte Carlo forecasting is that you obtain a complete distribution for future events, not just a point estimate and standard error. The simulation mean approximates the MMSE forecast. Use the 2.5th and 97.5th percentiles of the simulation realizations as endpoints for approximate 95% forecast intervals.