The confidence interval defines the range within which a forecasted value has some probability of occurring. Predictor uses an empirical method of calculating confidence intervals, using the standard error of forecasts:
For an m-period-ahead forecast, the error term rt(m) is defined as Yt – Ft(m), where Ft(m) is the m-period-ahead fit for period t.
The standard error of prediction for an m-period-ahead forecast is then expressed as
where n is the number of periods for which rt(m) is defined.
Assuming that forecast errors are normally distributed, the formula for predicting the future value of
at time t within a 95 percent confidence interval is
The empirical method is reasonably accurate when historical data amount is sufficiently large.