The Autocorrelation function is one of the widest used tools in timeseries analysis. It is used to determine **stationarity** and **seasonality**.

**Stationarity:**

This refers to whether the series is “going anywhere” over time. Stationary series have a constant value *over time. *

Below is what a *non*-stationary series looks like. Note the changing mean.

If a series is non-stationary (moving), its ACF may look a little like this:

The above ACF is “decaying”, or decreasing, very slowly, and remains well above the significance range (dotted blue lines). This is indicative of a non-stationary series.On the other hand, observe the ACF of a stationary (not going anywhere) series:

Note that the ACF shows exponential decay. This is indicative of a stationary series.Consider the case of a simple stationary series, like the process shown below:

We do not expect the ACF to be above the significance range for lags 1, 2, … This is intuitively satisfactory, because the above process is purely random, and therefore whether you are looking at a lag of 1 or a lag of 20, the correlation should be theoretically zero, or at least insignificant.

Next: ACF for **Seasonality**

Abbas Keshvani