Autocorrelation Function (ACF)

Computes ACF for a given series and plots correlogram.

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)

[Ana]

 

[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.

[MiguelMauricio]

Very useful, clear and easy to follow. Thank you

[Cristhiano Moreno]

Thank you.

How do you calculate the Bartlett bands ?

[Martin Dimkovski]

 

[Dmitry]

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