A tutorial note on the properties of ARIMA optimal forecasts

Abstract

Assuming an ARIMA(p,I,q) model represents the data, I show how optimal forecasts can be computed and derive general expressions for its main properties of interest. Namely, I present stepwise derivations of expressions for the variances of forecast errors, and the covariances between them at arbitrary forecasting horizons. Matricial forms for these expressions are also presented to facilitate computational implementation