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:
On the other hand, observe the ACF of a stationary (not going anywhere) 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
CoolStatsBlog 
thank you very much…..
Thank you Abbas for simple and well explained topic.
My question is in non-stationary data how can we find auto correlation? is partial auto correlation is a good alternative?
Hi Bahaa, thanks for the kind words. An autocorrelation for a non-stationary series would look funny, kinda of like here: https://coolstatsblog.files.wordpress.com/2013/08/berlin2.jpeg. Are you trying to prove that the realizations/values are correlated?
You’re welcome Amin 🙂
Hi Can you explain relation between Auto correlation and Confidence Interval with same intuitive explanation
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Hi Good simple explanation – I’ve always believed if you can explain simply – the person has understood it thoroughly 🙂 Came across the term an hour or so ago (ACF term) and was looking for a simpler explanation
And after a few hits – here it is 🙂
Rajesh
I agree, Rajesh. I think the best part about understanding something fully is that you can take control of the language around it, and therefore simplify it. Thanks for visiting!
Hi Abbas,
Just a non scientific comment to edit the post:
The word autocorrelation on the title is missspelled and needs a “L” 🙂
Thanks!
Can the acf be used to provide at least five comments about a series? If it is possible pls give me five of them
I am interested in knowing how do we assign the blue line in stationary series data
Hello,
a slight correction needed: MA(1) process is Y(t)=u(t)+b*u(t-1).
What you gave an example of above is a MA(0) process.
Good spot, Pranjal! It has been corrected. Thanks.
thanx sir, how can i get a pdf paper for this subject.
Thanks for this clarifying post!
The criteria for a stationary time series are (1) constant mean, (2) constant variance, (3) the covariance between today’s independent variable and tomorrow’s independent variable is not a function of time. In exactly what way does autocorrelation (correlation in the error terms) violate these three criteria?
awesome explanation… Thank you sir….
It helps a lot. Thanks!