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### Highlights from Autocorrelation Function (ACF)

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# Autocorrelation Function (ACF)

Computes ACF for a given series and plots correlogram.

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Description

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.

MATLAB release MATLAB 7.8 (R2009a)
23 Feb 2014

Thanks, this saved me a lot of time.

30 May 2013

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

27 Apr 2013
18 Jan 2013
08 May 2012

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

Hope that helps everyone

06 Dec 2011
21 Nov 2011

Thank you.

How do you calculate the Bartlett bands ?

16 Nov 2011

Very useful, clear and easy to follow. Thank you

11 Aug 2011

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.

03 Aug 2011