A tutorial note on the properties of ARIMA optimal forecasts

Galimberti, Jaqueson K. (2012): 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: optimal forecasts; forecasts properties; ARIMA
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Box, G. E. P., G. M. Jenkins, and G. C. Reinsel (2008). Time Series Analysis: Forecasting and Control (4th ed.). Wiley.

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.