Time Series Analysis: Method and Substance Introductory Workshop on Time Series Analysis

ACF/PACF Patterns

• AR models tend to fit smooth time series well, while MA models tend to fit irregular series well. Some series combine elements of AR and MA processes.
• Once we are working with a stationary time series, we can examine the ACF and PACF to help identify the proper number of lagged y (AR) terms and ε (MA) terms.

ACF/PACF

• A full time series class would walk you through the mathematics behind these patterns. Here I will just show you the theoretical patterns for typical ARIMA models.
• For the AR(1) model, │a1 │< 1 (stationarity) ensures that the ACF dampens exponentially.
• This is why it is important to test for unit roots before proceeding with ARIMA modeling.