ARIMA

General Notes

ARIMA = AutoRegressive Integrated Moving Average

• Related to ARMA

The "I" in ARIMA suggests the possibility of needing to use differencing to improve stationarity of the data.

Also sometimes referred to as Box-Jenkins Models.

Assumptions

Stationarity (weak stationarity) is a requirement for applying an ARIMA model.

Residuals of the model are iid N(0,s)

The residuals of the model should be white noise.

The coefficients associated with the AR and/or MA terms are related to the roots of polynomials that define the model. The polynomial roots should pass the Unit Root test.

ARIMA Diagnostic Tests

References

Texts

• Forecasting and Time Series - An Applied Approach (Bowerman)

• Introduction to Time Series Analysis and Forecasting (Montgomery)

Online Resources

• Forecasting: principles and practice (Hyndman)

• https://www.otexts.org/fpp/8/1 -- online text

• NIST - Box-Jenkins Approach