Monte Carlo Forecasting of Conditional Variance Models

Monte Carlo Forecasts

You can use Monte Carlo simulation to forecast a 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 forecast.

To forecast a process using Monte Carlo simulations:

Fit a model to your observed series using estimate.
Use the observed series and any inferred residuals and conditional variances (calculated using infer) for presample data.
Generate many sample paths over the desired forecast horizon using simulate.

Advantage of Monte Carlo Forecasting

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.