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.

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