Data Analysis with R, Second Edition - Second Edition

Uncertainty

The role of (and obstacles created by) uncertainty in forecasting is difficult to understate. Even if we could identify the deterministic patterns of a series as best as theoretically possible, there is still uncertainty in our forecasts due to random noise in our observed data, which will also be present in the future. In addition, there is uncertainty surrounding our proper identification of the patterns, or signal, of our series and our parameter estimates.

There's a time and a place for point forecasts, or forecasts that predict a single value of a variable for some future time, but we would often like some kind of measure of the uncertainty of our predictions. If we think of observations in time as realizations from a stochastic ...