After the model parameters are estimated, forecasts (predictions, prediction standard errors, and confidence limitsthe upper and lower values of a (usually 95%) confidence interval. In repeated sampling, approximately (1-alpha) 100% of the resulting intervals would contain the true value of the parameter that the interval estimates (where alpha is the confidence level associated with the interval).) are made using the model parameter estimates, the model residual variance, and the full range of data. If a model transformation was used, the forecasts are inverse transformed on a mean or median basis.
When it comes to decision-making based on the forecasts, the analyst must decide whether to base the decision on the predictions, lower confidence limits, upper confidence limits, or the distribution (predictions and prediction standard errors). If there is a greater penalty for over-predicting, the lower confidence limit should be used. If there is a greater penalty for under-predicting, the upper confidence limit should be used. Often for inventory control decisions, the distribution (mean and variance) is important.