Derivation of the Formula for a 95% Prediction Interval for an AR(1) Forecast

A common pitfall is confusing a prediction interval (for a single future observation

Y_{t+h}

) with a confidence interval (for the conditional mean

E[Y_{t+h}|\mathcal{F}_t]

or a model parameter). Students also frequently omit or miscalculate the cumulative variance contribution from past innovations, especially for

h > 1

Institutional Reference: Time Series Analysis