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Autocorrelation Function (ACF)

version 1.0 (2.01 KB) by

Computes ACF for a given series and plots correlogram.

17 Ratings



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Computes ACF for a given series. Returns a vector of autocorrelations through lag p. Also produces bar graph of autocorrelations, with rejection region bands for testing (under white noise assumption) each autocorrelation = 0.

Example: >> myacf = acf(y,12)

Does not require any toolboxes.

Comments and Ratings (19)


Alex (view profile)

Nice code! Thank you. Have you used this code for prediction of the next number in a series?

Thank u, very useful.

chen tai yu


Andres Kiani

Robin Szeto

Simple and nice!

Nakul Bansal

brilliant. Just one thing ... if you could make the bars thinner


harry (view profile)

thanks for your share, very useful.


Alan (view profile)

Thanks, this saved me a lot of time.


Fatima (view profile)

The code solved my problem after got confused with several other codes although I m so biginner and I had to be paitint to get it.
Thank you


Martin (view profile)


Dmitry (view profile)

Hey Calvin, ACFs produced by your code are biased towards zero...

The reason for that is that the first k elements in cross_sum (variable of the sub-function) are always zero. Also, dimensions of cross_sum after the loop in lines 104-106 are always Nx1. In large sample the bias is small but in small samples it might be sensible.

Given that matlab is very bad at handling loops it is better to avoid them altogether if possible. I adjusted your code by removing the sub-function completely, "global" attributes for N and ybar (lines 46 and 48) and substituting loop in lines 52-54 by

for i = 1:p
   yvar = (y-ybar)'*(y-ybar) ;
   ta(i) = (cross_sum / yvar)*(N/(N-i)) ;

Hope that helps everyone

Thank you.

How do you calculate the Bartlett bands ?

Very useful, clear and easy to follow. Thank you

Steven White

It did what I wanted it to do!

It might be nice to include a more meaningful example, rather than just an ACF of some random data.


Ana (view profile)

MATLAB Release
MATLAB 7.8 (R2009a)
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