I'm trying to understand how to interpret an autocorrelation function plot. I've been trying to find resources that explain how they are used and how to understand them but I haven't been able to find many articles.

This is what I understand (please feel free to correct me because I could easily be wrong):

- The autocorrelation function is similar (if not exactly) Pearson's correlation function defined for a single variable. So autocorrelation calculates the correlation between different time steps/lags within the same variable.
- Autocorrelation is a measure of the linear relationships between time steps/lags. If the current value of the time series is influenced by the previous value then I suppose the autocorrelation function would have some sort of decline from a high correlation to a low correlation? How would one know if the relationship between different time steps/lags is linear or non-linear? I know that if the series can be modelled by a linear function then it's linear; is that all there is to it?
- The plot can be used to determine if the series is random.
- The plot could be used to identify if there are seasonal trends in the series.

So here's how I think an autocorrelation function plot can be interpreted based on examples from here:

- The series is probably random if the correlation measurements lie within the confidence limits and there is no apparent pattern in the correlation.
- Weak autocorrelation if lag-1 has moderately high correlation which gradually decreases. The series is then moderately predictable.
- Strong autocorrelation if lag-1 has high autocorrelation and slowly declines and goes towards negative autocorrelation. The time series is usually high predictability.

Is that correct? I don't really understand the confidence lines in the plot (other than them being used to determine if the series is random). What do they indicate? Is it good if the confidence lines are near/basically zero? What should it be like?

Thank you for your time and consideration.

Regards

Pooven